: 


EXPOSITION  AND   ILLUSTRATION 
IN  TEACHING 


THE  MACMILLAN  COMPANY 

NKW  YORK    •    BOSTON  •    CHICAGO 
ATLANTA  •    SAN  FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON   -   BOMBAY  •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


EXPOSITION  AND  ILLUSTRATION 
IN  TEACHING 


BY 


JOHN   ADAMS,   M.A.,  B.Sc. 

PROFESSOR   OF   EDUCATION   IN   THE   UNIVERSITY 
OF   LONDON 


gork 

THE  MACMILLAN  COMPANY 
1910 

All  rights  reserved 


COPYRIGHT,  1910, 
BY  THE  MACMILLAN  COMPANY. 

Set  up  and  electrotyped.     Published  January,  1910. 


Jfortooolj 

J.  8.  Gushing  Co.  —  Berwick  A  Smith  Co. 
Norwood,  Mass.,  U.8.A. 


TO  MY  OLD  MASTER 
ME.  JAMES  LIDDELL 


2056238 


CONTENTS 

CHAPTER  PAOK 

I.  NATURE  AND  SCOPE  OF  EXPOSITION  AND  ILLUSTRA- 
TION         t        .  1 

II.  MENTAL  CONTENT .87 

III.  MENTAL  ACTIVITY «        .        .  65 

IV.  MENTAL  BACKGROUNDS .91 

V.  SUGGESTION 116 

VI.  CONDITIONS  OF  PRESENTATION      .        .        .        »        .  145 

VII.  BEGINNINGS  IN  EXPOSITION 167 

VIII.  ORDER  OF  PRESENTATION      .        .        .        .        ...  187 

IX.  EXEMPLIFICATION  AND  ANALOGY  .        .        .        .  228 

X.  THE  STORY  AS  ILLUSTRATION 250 

XL  ELABORATION 275 

XII.  DEGREE  IN  ILLUSTRATION 297 

XIII.  MATERIAL  ILLUSTRATIONS 317 

XIV.  THE  PICTURE  AS  ILLUSTRATION 336 

XV.  THE  DIAGRAM  AS  ILLUSTRATION 354 

XVI.  DANGERS  OF  ILLUSTRATION 391 

XVII.  THE  TORPEDO  SHOCK  .        .416 


vii 


.    V 

ii>.ar«ii.ul  HI 


EXPOSITION  AND  ILLUSTEATION 
™'       IN  TEACHING 

CHAPTER  I 

NATURE  AND  SCOPE  OF  EXPOSITION  AND 
ILLUSTRATION 

APPLYING  the  principles  to  be  laid  down  in  what  fol- 
lows, it  is  well  to  make  a  beginning  in  some  region  of 
knowledge  that  is  common  to  all  intelligent  educated 
people.  A  good  dictionary  may  be  fairly  taken  to 
represent  such  a  region.  What  the  dictionary  tells  us 
about  Exposition  and  Illustration  will  probably  be 
admitted  to  be  common  property,  and  therefore  a  suit- 
able starting-point  for  a  treatment  that  will  introduce 
points  of  view  that  may  be  unfamiliar  to  the  reader.  In 
teaching,  it  is  now  generally  admitted  that  we  ought 
rather  to  lead  up  to  a  definition  than  to  start  from  one. 
In  what  follows,  the  definitions  as  found  in  the  diction- 
ary will  not  be  treated  as  ends  in  themselves,  but  merely 
as  the  common  basis  from  which  reader  and  writer  may 
make  an  intelligible  start.  This  chapter  will  concern 
itself  not  so  much  with  the  explanation  of  the  defini- 
tions which  it  borrows  from  the  dictionary  as  with  the 
elaboration  of  the  connotation  of  the  terms  Exposition 
and  Illustration  in  their  relation  to  teaching. 

In  Sir  James  A.  H.  Murray's  "New  English  Diction- 


2       EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

ary  on  Historical  Principles"  we  find  under  the  word 
expound,  the  following  meanings :  — 

1.  To  set  forth,  declare,  state  in  detail  (doctrines,  ideas,  principles ; 

formerly  used  with  wider  application). 

2.  To  explain,  interpret : 

(a)  gen.  To  explain  (what  is  difficult  or  obscure) ;  to  state 
the  signification  of ;  to  comment  on  (a  passage  or  an  author) . 

(b)  esp.   To  interpret,  comment  upon   (Scripture,  religious 
formularies,  etc.).     Now  chiefly  with  reference  to  homiletic 
exposition. 

We  may  safely  neglect  the  more  literal  meanings 
attached  to  exposition,  such  as  "putting  out  of,"  " ex- 
posure," " putting  to  public  view";  just  as  we  need  not 
seriously  consider  the  archaic  use  in  Hudibras:  "He 
expounded  both  his  pockets,"  or  Littre's  "putting  in 
the  pillory."  So  far  as  the  teacher  is  concerned,  two  of 
the  accepted  meanings  stand  out  as  of  importance:  "to 
set  forth"  and  "to  explain  or  interpret."  In  the  ordi- 
nary practice  of  the  schoolroom  these  two  meanings  are 
not  usually  distinguished  from  each  other,  because,  as  a 
matter  of  fact,  the  purpose  of  setting  forth  anything  is 
to  explain  it  to  the  pupil.  If  we  set  a  matter  clearly 
before  another,  we  feel  that  we  have  explained  it.  If 
to  a  wayfarer  we  set  forth  his  route,  we  feel  that  we  have 
explained  a  matter  about  which  he  was  in  doubt.  A 
clear  statement  of  the  Binomial  Theorem  is  generally 
regarded  as  in  some  sort  an  explanation  of  that  theorem. 
There  are  those  who  question  whether  the  teacher  can 
under  any  circumstances  do  more  than  make  just  such 
a  presentation.  Jacotot,  the  founder  of  the  "Universal 
Method"  of  teaching,  is  usually  true  to  his  reiterated 
principle  that  "a  teacher  is  never  necessary  to  man," * 

1  Enseignement  Universd,  p.  304. 


NATURE  AND  SCOPE  3 

but  in  a  moment  of  unusual  generosity  he  admits  that 
"a  teacher  is  useful  to  men,  he  is  necessary  to  children, 
but  a  teacher  who  explains  [un  maitre  explicateur]  is 
deadening  [abrutissant]." 1  The  negativeness  of  the 
teacher's  work  from  this  point  of  view  is  obvious.  In 
the  words  of  one  of  Jacotot's  editors:  "In  fact,  the 
Founder  limits  himself  to  saying:  'Here  is  a  book; 
learn  Latin.' ' 

But  while  the  two  meanings  of  Exposition  —  setting 
forth  and  explaining  —  to  a  certain  extent  overlap, 
they  imply  a  real  distinction  that  is  worth  the  teacher's 
attention.  While  we  are  mainly  interested  in  discover- 
ing how  to  present  certain  matters  in  the  way  best 
suited  to  render  them  intelligible  to  the  pupil,  we  are 
none  the  less  setting  them  forth.  The  first  meaning  of 
Exposition,  hi  fact,  implies  the  presentation  of  new 
matter,  the  second  the  explanation  or  interpretation  of 
matter  already  known  to,  but  not  yet  fully  understood 
by,  the  pupil.  The  first  meaning,  "setting  forth," 
corresponds  to  what  is  usually  understood  in  school 
and  college  by  the  verb  demonstrate.  This  word,  which 
literally  means  to  show  or  point  out,  has  acquired  the 
added  connotation  of  "for  a  purpose."  A  demon- 
strator in  a  college  is  not  a  man  who  points  out  merely, 
but  one  who  shows  the  meaning  of  what  he  points  out. 
As  the  dictionary  has  it,  he  "exhibits  and  explains." 
Still,  the  fact  remains  that  in  both  the  first  meaning  of 
expound  and  in  the  general  meaning  of  demonstrate 
there  is  the  notion  of  supplying  new  matter,  so  that  this 
presentation  of  new  matter  may  be  regarded  as  an  es- 
sential part  of  Exposition,  though  it  need  not  be  found 
at  all  stages  of  Exposition.  We  shall  see  when  we  come 
1  Avant-propos  de  cette  Quatrieme  Edition :  De  la  Langue  maternelle. 


4        EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

to  deal  with  Illustration  that  the  same  distinction  arises 
between  the  introduction  of  new  matter  and  the  manip- 
ulation of  old. 

It  has  to  be  observed  that  for  our  present  purpose  we 
are  treating  the  subject  of  Exposition  from  the  point  of 
view  of  the  teacher.  It  is  possible  to  regard  it  entirely 
from  the  pupil's  standpoint.  When  this  is  done,  Ex- 
position is  dealt  with  as  a  part  of  composition,  and 
ranks  as  coordinate  with  narration  and  description. 
As  such  it  enters  into  the  ordinary  school  curriculum, 
and  in  many  cases  receives  a  considerable  amount  of 
attention.  Naturally  the  principles  of  Exposition  must 
remain  the  same  whether  practised  by  the  pupil  or  by 
the  teacher,  but  the  conditions  under  which  the  princi- 
ples are  applied  hi  the  two  cases  are  so  different  that  a 
separate  treatise  is  required  for  each.1 

It  will  be  noted  that  the  dictionary  lays  stress  on  the 
fact  that  the  things  to  be  set  forth  are  "doctrines,  ideas, 
principles,"  the  obvious  inference  being  that  Exposition 
has  nothing  to  do  with  material  things,  that  we  can  no 
more  expound  a  steam  engine  than  we  can  expound  our 
pockets.  But  while  it  is  bad  English  to  speak  of  ex- 
pounding a  locomotive,  we  may  correctly  speak  of 
expounding  the  principles  on  which  the  locomotive 
works.  This  does  not,  after  all,  mean  that  the  concrete 
is  removed  from  the  realm  of  Exposition,  but  merely 
that  Exposition  can  deal  with  the  concrete  only  in  terms 
of  ideas.  The  contributions  of  the  senses  must  be 
taken  for  granted  by  the  expositor.  His  business  is  so 
to  arrange  the  mental  results  of  sensations  that  they 

1  For  a  treatment  of  the  subject  as  a  part  of  the  curriculum,  see 
Exposition  in  Classroom  Practice,  by  Mitchill  and  Carpenter,  the  Mac- 
millan  Co.,  New  York,  1906. 


NATURE  AND  SCOPE  5 

shall  form  a  well-organised  and  therefore  intelligible 
whole.  From  this  point  of  view  all  Exposition  is 
explanation  or  interpretation,  though  in  order  to  com- 
plete the  explanation  it  may  be  necessary  to  place  the 
pupil  in  such  a  position  that  new  matter  may  be  as- 
similated. Sometimes  the  expositor  can  so  arrange  old 
matter  that  it  becomes  intelligible  without  the  intro- 
duction of  anything  new,  but  frequently  it  happens 
that  hi  the  pupil's  knowledge  there  is  some  link  lack- 
ing, without  which  all  the  present  material  is  necessa- 
rily unintelligible.  To  introduce  the  missing  elements 
is  clearly  an  essential  part  of  Exposition.  I  have 
known  a  man  who  had  a  really  excellent  knowledge 
of  French  completely  puzzled  by  a  passage  that  pre- 
sented no  apparent  difficulty.  He  could  make  no  sense 
out  of  it  because  he  did  not  happen  to  know  that 
Monsieur,  when  used  absolutely,  meant  the  eldest 
brother  of  the  king  of  France. 

It  is  worth  remarking  that  in  this  connection "  ex- 
planation" has  no  reference  to  the  ultimate  meaning 
of  the  matter  to  be  dealt  with.  It  is  not  a  metaphysical 
term.  Accordingly,  from  the  teacher's  point  of  view, 
Exposition  does  not  include  the  discovery  of  the  true 
meaning  of  the  matter  to  be  expounded,  but  only  the 
setting  forth  of  that  matter  in  such  a  way  as  to  be  in- 
telligible to  the  pupil.  The  facts  and  the  explanation 
of  the  facts  are  for  the  teacher  the  data  of  Exposition. 
He  may  be  misinformed  about  the  materials  he  is  deal- 
ing with,  his  facts  may  not  be  facts,  his  explanations 
of  his  facts  may  not  stand  the  test  of  investigation, 
and  yet  his  exposition  may  be  excellent.  As  an  ex- 
positor his  business  is  so  to  present  his  facts  that  they 
shall  carry  with  them  the  explanation  that  appeals  to 


6       EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

him  as  satisfactory.  Too  often  it  has  been  assumed 
that  an  intelligent  mastery  of  the  facts  to  be  presented 
is  enough  to  qualify  a  teacher  for  his  work.1  In  reality 
it  is  no  more  than  the  essential  condition  of  his  begin- 
ning to  learn  to  apply  his  art.  For  our  present  purpose 
we  shall  assume  that  the  teacher  has  acquired  the 
necessary  facts  and  has  mastered  their  meaning.  The 
problem  remains  to  communicate  these  facts  so  that 
they  shall  convey  to  the  pupil  the  meaning  the  teacher 
has  accepted  as  the  true  one. 

The  teacher  may  not  only  adopt  a  wrong  interpre- 
tation of  the  facts,  but  may  know  that  his  interpreta- 
tion is  false,  and  yet  be  an  excellent  expositor.  Pro- 
fessor J.  W.  Allen 2  provides  an  admirable  illustration. 
Taking  the  Reformation  as  subject,  he  gives  three  sep- 
arate expositions  of  its  meaning,  one  from  the  Roman 
Catholic  point  of  view,  another  from  the  Protestant, 
while  the  third  is  written  from  the  standpoint  of  a 
critical  Mercutio  who  calls  for  "a  plague  o'  both  your 
houses."  By  appropriate  overemphasis  and  com- 
pression, each  of  the  accounts,  while  not  inventing 
incidents  or  what  are  commonly  called  "facts,"  con- 
trives to  convey  an  entirely  different  impression  from 
the  others.  So  far  as  each  is  successful,  it  leaves  the 
mind  of  the  pupil  with  his  ideas  of  the  Reformation 
reconstructed  in  a  particular  way,  a  way  that  was  first 
developed  hi  the  mind  of  the  expositor,  though,  as 
we  see,  he  has  adopted  at  least  two  other  modes  of 
reconstructing  the  available  elements. 

1  Cf .  De  Quincey :  "  The  rb  docendum,  the  thing  to  be  taught,  has 
availed  to  obscure  or  even  to  annihilate  for  their  eyes  every  anxiety 
as  to  the  mode  of  teaching."  Essay  on  Style.  Collected  Writings 
(Masson,  1897),  Vol.  II,  p.  160. 

J  The  Place  of  History  in  Education,  1909,  p.  210. 


NATURE  AND  SCOPE  7 

The  test  of  the  expositor  is:  does  he  produce  on 
the  mind  of  the  pupil  the  impression  he  desires  to  pro- 
duce ?  Literary  style  is  sometimes  tested  by  the  clear- 
ness with  which  it  conveys  the  author's  meaning.  But 
sometimes  the  author  may  not  desire  that  his  mean- 
ing should  be  understood.  He  may  want  his  words  to 
convey  one  meaning  to  one  set  of  readers  and  another 
to  another.  From  this  point  of  view  the  test  is:  does 
he  convey  the  meaning  to  each  that  he  intended  to 
convey  ?  Style  is  not  so  much  a  means  of  making  an- 
other know  what  we  think,  as  it  is  a  means  of  producing 
a  certain  effect  upon  the  mind  of  another.  So  in  the 
case  of  the  expositor,  whether  he  be  honest  or  dishonest, 
the  result  of  successful  exposition  must  be  that  there 
now  exists  in  the  mind  of  the  hearer  or  reader  a  com- 
bination of  mental  elements  that  previously  existed  in 
the  mind  of  the  expositor.  There  may  be  many  other 
ways  in  which  the  elements  could  be  combined,  and 
these  possible  combinations  may  all  have  been  formed 
at  one  time  or  other  in  the  mind  of  the  expositor,  but 
if  he  has  succeeded  hi  his  present  work,  only  one  of  these 
combinations  is  able  to  establish  itself  in  the  mind  of 
the  person  he  is  dealing  with.  Exposition,  therefore, 
comes  to  be,  in  the  ultimate  resort,  the  manipulation 
of  the  ideas  of  another. 

This  gives  a  more  definite  meaning  to  the  term  ex- 
planation as  used  by  the  teacher.  Some  people  do  not 
see  how  things  can  be  explained.  They  admit  the  ad- 
vantage of  statement  and  demonstration,  but  cannot 
see  how  something  that  has  been  stated  and  demon- 
strated can  be  made  clearer  by  writing  or  talking  about 
it.  They  quote  the  case  of  the  little  girl  who  has  won 
the  good-will  of  all  the  teachers'  common  rooms  in  the 


8       EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

world  by  her  protest  that  she  thought  she  could  under- 
stand her  arithmetic  if  only  her  mother  would  give 
up  explaining  it.1  In  his  Modern  Painters,  Ruskin 
tells  us  bluntly:  "Explanations  are  wasted  time.  A 
man  who  can  see,  understands  a  touch;  a  man  who 
cannot,  misunderstands  an  oration."  The  contrast 
between  a  touch  and  an  oration  is  not  very  happy,  as 
it  might  be  held  to  imply  a  comparison  between  two 
different  kinds  of  explanation  —  practical  and  verbal. 
But  even  if  we  limit  the  contrast  to  the  cognate  terms, 
a  word  and  an  oration,  we  have  still  the  implied  admis- 
sion that  the  word  has  done  some  good.  In  actual  ex- 
perience it  is  often  found  that  only  a  word  is  needed  to 
establish  the  proper  relation  among  a  group  of  ideas  that 
need  nothing  but  the  help  of  this  word  to  reduce  them- 
selves to  a  combination  intelligible  to  a  person  who 
otherwise  is  unable  to  understand  them.  It  is  quite 
possible  for  a  man  to  have  hi  his  mind  all  the  facts 
necessary  to  explain  something  that  he  does  not  under- 
stand, and  yet  be  quite  unable  to  make  the  necessary 
application  of  his  knowledge.  The  facts  must  be  put 
in  a  certain  order  before  the  true  relation  can  be  seen, 
and  it  is  the  business  of  the  expositor,  by  means  of 
words  or  otherwise,  to  arrange  them  in  this  order. 

One  of  the  great  difficulties  at  certain  examinations 
is  to  keep  candidates  from  getting  just  this  kind  of 
help  from  each  other.  A  difficult  problem  in  Perspec- 
tive or  in  Orthographic  Projection  often  becomes  quite 
easy  to  a  candidate  from  a  single  glance  at  his  neigh- 

1  In  his  Charles  Dickens,  Mr.  G.  K.  Chesterton  says :  Dickens  "  had 
one  most  unfortunate  habit,  a  habit  that  often  put  him  in  the  wrong, 
even  when  he  happened  to  be  in  the  right.  He  had  an  incurable 
habit  of  explaining  himself." 


NATURE  AND  SCOPE  9 

hour's  completed  drawing,  though  without  that  glance 
he  could  make  no  sense  out  of  the  problem  as  stated  in 
words  on  his  examination  paper.  He  has  all  the  knowl- 
edge needed  to  work  out  the  problem,  but  he  lacks  the 
power  of  making  the  initial  combination.  At  a  certain 
examination  in  Applied  Mathematics  an  industrious 
but  not  very  original  student  found  herself  unable  to 
understand  a  particular  question  on  her  paper  till  she 
chanced  to  see  a  fellow-candidate  twirling  her  finger  in 
a  particular  way.  The  motion  of  the  finger  at  once 
suggested  the  idea  of  a  left-handed  helix,  and  the  point 
of  the  question  became  plain.  Both  candidates  hap- 
pened to  be  considering  the  same  problem  at  the  time, 
but  there  was  no  intentional  signalling.  The  clever 
candidate  did  not  know  that  she  had  helped  the  other. 
It  has  to  be  remembered  that  unless  the  duller  student 
had  had  the  necessary  materials  in  her  mind,  no  amount 
of  finger-twirling  would  have  been  of  the  slightest  use 
to  her. 

In  a  similar  way  an  unintelligent  plumber  has  often 
in  his  mind  all  the  facts  that  are  necessary  to  the  mas- 
tery of  a  difficult  job  in  a  house,  and  is  yet  unable  to 
apply  his  knowledge.  The  householder  makes  several 
suggestions,  most  of  them  futile,  but  happens  to  hit 
upon  one  combination  that  appeals  to  the  practical 
but  unintelligent  workman,  who  then  exclaims,  "Ah, 
now  that  you  put  it  that  way — , "  and  proceeds  to 
carry  out  a  suggestion  that  he  could  not  originate.  In 
a  certain  sense  the  ignorant  householder  has  explained 
matters  to  the  plumber.  What  the  householder  has 
done  more  or  less  by  chance,  the  skilful  expositor  must 
do  deliberately. 

Exposition  may  well  be  described  as  a  bipolar  pro- 


10     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

cess.  For  our  own  ends  we  may  regard  it  now  from 
the  point  of  view  of  the  expositor,  and  now  from  that 
of  the  person  to  whom  something  is  being  expounded. 
But  the  process  is  working  from  both  sides  all  the  time. 
It  is  interesting  to  note  that  at  the  present  moment 
psychologists  are  feeling  keenly  the  need  for  double 
terms  in  the  case  of  similar  bipolar  processes.1  In 
suggestion  and  imitation,  for  example,  we  have  the 
two  poles  of  the  process  and  a  term  to  describe  only  one 
of  them.  Suggester  and  imitator  are  words  that  stand 
for  the  persons  who  suggest  or  imitate;  but  we  have  no 
terms  to  denote  those  who  are  imitated  or  to  whom 
suggestion  is  made.  In  the  books  we  find  rather  clumsy 
references  to  the  subject,  the  patient,  the  pattern,  the 
model.  Sometimes  it  is  proposed  to  follow  certain 
analogies  and  boldly  introduce  the  two  terms,  suggestee 
and  imitatee.  But  apart  from  the  barbarous  sound  of 
expositee  or  expositatee,  there  is  the  serious  objection 
that  this  form  overemphasises  the  passive  element. 
The  person  to  whom  an  exposition  is  being  made  is  to 
a  certain  extent  more  passive  than  is  the  expositor, 
but  he  is  far  from  being  quite  passive.  He  is  guided  by 
the  expositor,  and  to  that  extent  plays  a  passive  part, 
but  if  the  exposition  is  to  be  successful,  the  person  to 
whom  the  expositor  appeals  must  bestir  himself,  and 
react  vigorously  on  the  material  supplied  by  the  ex- 
positor. 

In  what  follows  we  shall  have  to  make  constant 
reference  to  "the  person  to  whom  the  exposition  is  to 
be  made,"  and  it  is  obvious  that  this  cumbrous  peri- 
phrasis cannot  be  repeated  on  every  occasion.  So 
with  "the  matter  to  be  expounded."  In  both  cases 

1  Cf.  Mr.  W.  Macdougall's  Social  Psychology,  p.  325. 


NATURE  AND   SCOPE  11 

we  require  a  technical  term.  With  regard  to  the  matter 
to  be  expounded,  we  seem  to  have  a  word  to  our  hand. 
Sheltering  under  the  authority  of  De  Quincey's  use  of 
TO  docendum,  the  thing  to  be  taught,  we  would  sug- 
gest the  term  expositandum,  the  thing  to  be  expounded. 
By  dropping  the  Greek  TO  we  render  the  term  a  little 
less  formidable,  and  lose  nothing  in  the  way  of  accuracy. 
We  have  seen  that  no  such  convenient  term  suggests 
itself  for  the  person  to  whom  the  exposition  is  to  be  made. 
Probably  it  will  be  best  to  retain  the  ordinary  word 
pupil.  To  be  sure,  the  word  is  not  commonly  applied 
to  a  person  who  has  left  school,  and  we  must  in  these 
pages  apply  it  on  occasion  to  people  of  quite  mature 
years  and  high  attainments;  but  no  confusion  need 
arise  if  we  clearly  understand  that  by  pupil  we  shall 
in  this  book  indicate  the  person  who  in  the  process  of 
Exposition  occupies  the  pole  that  is  the  correlate  of  the 
expositor-pole.  After  all,  a  learned  professor  receiv- 
ing instruction  from  a  street  urchin  how  to  find  his 
way  back  to  his  hotel  is,  for  the  time  being,  a  pupil. 

Our  first  business  in  preparing  this  ordinary  term 
pupil  for  our  use  is  to  get  rid  of  the  lingering  notion  that 
it  represents  a  purely  passive  side  of  the  process  of 
learning.  It  connotes  rather  that  the  person  is  being 
directed  in  his  activities  than  that  he  ceases  to  be  active. 
We  are  prone  to  regard  listening  as  in  itself  a  passive 
matter.  The  audience  is  conspicuously  passive,  while 
the  lecturer  or  preacher  is  as  conspicuously  active. 
Preaching  has,  hi  fact,  been  defined  as  "an  animated 
dialogue  with  one  part  left  out."  But  this  part  that. 
is  left  out  as  spoken  word  must  certainly  be  supplied 
as  inner  thought  alj  through  the  sermon;  else  the 
preaching  is  a  complete  failure.  The  difference  be- 


12     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

tween  teaching  and  lecturing  lies  just  here.  No  fault 
is  more  common  among  inexperienced  teachers  than  the 
tendency  to  do  all  the  talking,  and  to  treat  the  pupils 
as  mere  sleeping  partners  in  the  work  of  the  class. 
"Too  much  of  a  lecture"  is  the  hardest  worked  cliche 
in  the  Normal  master's  repertory  of  critical  phrases.1 
In  class  work  the  one  part  must  not  be  left  out.  There 
must  be  give  and  take ;  the  pupils  must  be  allowed  not 
only  to  be  active,  but  to  show  their  activity.  In  Ex- 
position the  teacher  may  work  either  by  the  way  of 
open  dialectic,  the  rapid  interchange  of  question  and 
anstver,  or  by  the  more  sedate  methods  of  the  lecture. 
The  important  point  to  note  is  that  the  pupil  must  be 
equally  active  in  either  case.  The  psychology  of  listen- 
ing has  not  been  sufficiently  considered  by  teachers. 

To  begin  with,  we  are  inclined  to  regard  listening  as 
more  continuous  than  it  really  is.  Psychologists  are 
laying  more  and  more  stress  on  the  rhythmic  element 
in  the  phenomena  in  which  they  are  interested.  No- 
where is  this  rhythmic  element  more  prominent  than 
in  listening,  especially  when  long  periods  are  considered. 
Trained  listeners,  such  as  students  who  have  reached 
the  postgraduate  stage,  are  able  to  listen  with  a  fair 
degree  of  continuity  throughout  an  hour's  discourse; 

1  It  is  interesting  to  note  that  in  England  the  inevitable  reaction 
has  come.  So  thoroughly  have  students  in  training  been  drilled  into 
a  distrust  of  lecturing  that  they  are  now  said  to  be  losing  the  power  of 
sustained  speech.  "Few  of  our  recently  trained  teachers,"  says  Pro- 
fessor Mark  Wright,  "  can  make  a  well-arranged  verbal  presentation  to 
a  class  for  ten  minutes,  without  asking  questions."  It  would  certainly 
be  a  pity  if  teachers  lost  the  power  of  consecutive  presentation,  but 
of  the  two  the  loss  of  this  power  of  lecturing  would  be  much  less  seri- 
ous than  the  loss  of  the  power  of  conducting  class  work  on  the  lines 
of  a  vigorous  dialectic.  Fortunately,  in  America,  there  is  little  danger 
of  the  loss  of  sustained  speech. 


NATURE  AND  SCOPE  13 

but  your  ordinary  amateur  listener,  say  the  man  who 
confines  himself  to  a  sermon  a  week  and  an  occasional 
popular  lecture,  hears  only  in  patches.  Salient  points  in 
the  discourse  stand  out,  but  each  of  these  is  a  point  of 
departure  for  trains  of  thought  not  bargained  for  by  the 
speaker.  The  untrained  listener  rushes  off  from  each 
salient  point  —  and  often  from  points  that  are  not  at 
all  salient  from  the  speaker's  point  of  view  —  in  a 
direction  determined  by  the  acquired  content  of  his 
own  mind,  and  he  is  recalled  only  by  the  emergence  of 
another  point  in  the  lecture  that  catches  his  wandering 
attention. 

Fortunately,  what  is  true  in  interstitial  vision  is  true 
here.  Just  as  the  mind  fills  in  a  great  many  of  the  gaps 
that  occur  hi  actual  vision,  so  it  fills  hi  a  great  many 
gaps  that  occur  in  the  hearing  of  a  discourse.  Even 
dull  people  who  are  in  earnest  about  the  sermon  go 
away  with  some  fairly  complete  general  idea  of  the 
whole  (it  is  taken  for  granted  that  there  is  a  general 
idea  underlying  the  whole),  but  in  many  cases,  no  doubt, 
even  after  honest  attention,  the  inexperienced  listener 
goes  away  with  only  one  or  two  prominent  points,  which 
are  not  by  any  means  necessarily  points  in  the  main 
line  of  thought,  but  are  more  likely  to  be  prominent 
points  of  illustration. 

A  training  in  the  art  of  listening  is  therefore  an  im- 
portant part  of  Exposition.  Unless  the  expositor  can 
assure  himself  that  his  pupils  are  doing  their  share  of  the 
work,  he  must  be  very  doubtful  about  his  success.  In 
class-teaching  he  will,  of  course,  seize  every  opportunity 
of  making  the  pupils  take  an  overt  share  in  the  work; 
but  in  the  case  of  a  more  or  less  formal  lecture  this  is 
difficult,  sometimes,  indeed,  impossible;  so  the  lecturer 


14     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

must  do  what  he  can  to  encourage  the  pupils  to  test 
their  powers  of  continuous  attention.  An  excellent 
test  that  they  can  themselves  apply  is  to  see  how  far 
they  can  anticipate  what  is  coming.  Certain  lecturers 
resent  such  a  test.  I  have  known  one  quite  lose  his 
temper  when  this  matter  was  brought  before  him.  He 
did  not  put  it  that  way,  but  his  view  obviously  was  that 
nobody  could  anticipate  what  he  was  going  to  say  in 
any  of  his  lectures.  But  the  test  implies  no  challenge 
of  the  lecturer's  originality.  No  doubt  at  the  very 
beginning  of  an  isolated  lecture  by  an  unknown  person, 
one  cannot  usually  anticipate  what  is  coming,  and, 
further,  at  many  points  in  the  lecture  one  may  be  quite 
unable  to  guess  what  is  coming  next.  But  in  an  ordi- 
nary lecture  or  sermon  the  experienced  listener  is  gen- 
erally able  to  anticipate  a  great  deal  of  what  is  com- 
ing. When  a  halting  speaker  hesitates  for  a  word, 
there  are  usually  scores  of  his  hearers  who  have  already 
supplied  it. 

What  the  psychologist  points  out  to  us  in  our  ordi- 
nary reading  of  a  book  or  newspaper  is  true  in  our  listen- 
ing. In  almost  every  case  the  incidence  of  attention 
is  not  on  the  word  that  occupies  the  centre  of  the  field 
of  vision.1  So  hi  music  we  are  familiar  with  the  fact 
that  the  performer's  eye  is  frequently  bars  ahead  of 
the  note  he  is  actually  striking,  and  in  certain  familiar 
combinations  the  conclusion  of  a  passage  seems  to  come 
of  its  own  accord,  even  when  the  notes  are  not  seen  at 

1  Dealing  with  reading  aloud,  Mr.  E.  V.  Lucas,  in  The  Author  for 
July,  1909,  writes  the  suggestive  words:  "Lacking  the  needful  power 
of  seeing  two  lines  ahead  (as  John  Roberts  used  to  see  two  cannons 
ahead),  I  am  continually  falling  into  wrong  stresses  and  misunder- 
standings, which  annoy  me  like  little  stings." 


NATURE  AND  SCOPE  15 

all ;  that  is  to  say,  certain  common  endings  will  be  played 
quite  naturally  by  the  performer,  even  if  the  notes  oc- 
cur on  the  page  that  has  not  yet  been  exposed.  We  are 
too  apt  to  assume  that  our  reading  and  our  listening 
are  matters  of  word  by  word  understanding.  Our 
thinking  is  not  carried  on  in  this  atomistic  way.  We 
work  with  much  bigger  units  than  the  individual  word 
or  sound.  We  can  never  know  the  present  except  in 
relation  to  the  past  and  the  future.  In  the  stream 
of  thoughts  that  pass  through  our  minds  the  present 
thought  is  the  darkest  in  the  whole  series  :  — 

"The  knowledge  of  some  other  part  of  the  stream,  past  or  future, 
near  or  remote,  is  always  mixed  in  with  our  knowledge  of  the 
present  thing." l 

When  Shakespeare  and  Shelley  agree  in  selecting  as 
man's  high  prerogative  the  power  of  "  looking  before 
and  after,"  they  are  building  on  a  sound  psychological 
foundation.  The  present  can  be  understood  only  by 
reference  to  the  past  and  the  future. 

In  listening,  the  pupil  should  always  be  using  the  past 
to  anticipate  the  future.  The  beginning  and  ending 
of  good  listening  is  anticipation  —  being  able  to  project 
ourselves  towards  the  point  up  to  which  the  lecturer 
is  leading.  We  may  not  be  able  to  anticipate  the  lec- 
turer sentence  by  sentence.  It  may  be  that  we  are 
unable  to  complete  such  a  sentence  as  "The  most  op- 
timistic writer  on  Education  is ."  Here  it  is  prob- 
able that  very  few  could  add  the  missing  word  in  the 
sentence  as  it  thus  occurs  out  of  the  blue.  But  sup- 
pose this  sentence  occurs  in  the  middle  of  a  lecture,  a 
good  lecture  —  that  is,  a  lecture  that  has  been  thought 

1  W.  James :  Principles  of  Psychology,  Vol.  I,  p.  606. 


16     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

out  and  organised  —  there  would  have  been  in  all 
probability  indications  by  the  help  of  which  an  expe- 
rienced listener  could  infer  at  least  the  category  under 
which  the  individual  name  is  to  be  found.  So  far  from 
being  a  reflection  on  the  lecturer's  originality,  it  is  the 
highest  compliment  to  him  that  his  audience  should 
be  able  to  anticipate,  within  limits,  what  is  coming. 
It  is  your  careless,  unprepared,  unmethodical  man  who 
says  the  unexpected  things.  For  remember,  even  with 
a  professional  dealer  in  paradoxes,  it  is  quite  possible, 
by  the  rule  of  contraries,  or  hi  extreme  cases,  when  that 
rule  fails,  by  the  rule  of  contra-contraries,  to  anticipate 
what  he  is  going  to  say.  In  other  words,  an  organised 
lecture  has  a  style  underlying  it  that  is  all  in  the  whole 
and  all  in  every  part,  and  that  style  can  be  surprised 
by  a  sympathetic  listener.  A  merely  capricious  lecture, 
on  the  other  hand,  has  nothing  by  which  its  develop- 
ment may  be  followed. 

Note  further  that  the  essential  thing  is  not  so  much 
that  the  pupil  is  to  be  able  to  anticipate  the  very  points 
to  be  raised,  and  how  they  will  be  settled,  as  that  he 
must  adopt  the  anticipative  attitude.  The  pupil- 
mind  must  be  feeling  its  own  way  into  the  problems 
that  are  being  dealt  with,  and  must  keep  on  asking 
itself  questions  about  the  possibilities  of  the  case. 
It  may  be  thought  that  this  stretching  out  of  the  mind 
towards  what  is  to  come  will  render  it  oblivious  to  what 
has  gone  before,  that  it  will  be  so  busy  with  the  future 
as  to  lose  sight  of  the  past.  On  the  contrary,  it  is  only 
by  relying  upon  the  past  that  the  mind  has  any  chance 
of  anticipating  the  future.  The  really  active  mind  is 
playing  all  round  the  subject  it  is  examining,  and  from 
what  has  been  already  presented,  it  gets  all  manner  of 


NATURE   AND  SCOPE  17 

impulses  urging  it  to  make  tentative  advances  in  this 
direction  and  in  that.  Each  advance  is  not  only  sug- 
gested by  what  has  gone  before,  but  must  be  tested 
by  its  consistency  with  the  facts  that  have  suggested  it. 
Assuming  that  the  ultimate  purpose  of  Exposition 
is  to  cause  to  arise  in  the  mind  of  the  pupil  a  combina- 
tion of  ideas  exactly  corresponding  to  a  combination 
already  formed  in  the  mind  of  the  expositor,  it  is  clearly 
of  the  first  importance  to  find  out  what  means  are  at 
our  disposal  to  bring  about  this  combination  in  the 
pupil's  mind.  This  demands  a  study  of  the  nature  of 
ideas  and  the  laws  according  to  which  they  act.  But 
before  entering  upon  details,  it  is  well  to  get  a  general 
view  of  the  whole  ground.  In  ordinary  language  we 
use  the  word  Illustration  as  meaning  the  clearing  up 
of  something  that  is  in  itself  obscure.  This  idea  we 
found  to  underlie  also  the  meaning  of  Exposition.  In 
point  of  fact,  there  is  a  certain  confusion  in  the  popular 
use  of  these  two  terms,  a  confusion  that  has  a  good  deal 
to  justify  it  in  the  usage  of  capable  writers.  Appealing, 
as  in  the  case  of  the  term  Exposition,  to  the  disinterested 
verdict  of  the  dictionary,  and,  in  order  to  widen  our 
outlook,  selecting  an  American  lexicographer,  we  find 
that  Webster  thus  delivers  himself  on  the  meanings  of 
the  verb  to  illustrate  :  — 

1.  To  make  clear,  bright,  or  luminous. 

2.  To  set  in  a  clear  light ;  to  exhibit  distinctly  or  conspicuously. 

3.  To   make    clear,   intelligible,    or    apprehensible;  to    elucidate, 

explain,  or  exemplify,  as  by  means   of   figures,  comparisons, 
and  examples. 

4.  To  adorn  with  pictures,  as  a  book  or  subject;  to  elucidate 

with  pictures,  as  a  history  or  romance. 

5.  To  give  renown  or  honor  to ;  to  make  illustrious ;  to  glorify. 

c 


18     EXPOSITION   AND  ILLUSTRATION    IN  TEACHING 

The  first  meaning  is  purely  literal,  as  shown  in  the 
line  quoted  from  Chapman:  "Here  when  the  moon 
illustrates  all  the  sky,"  and  does  not  interest  us  here. 
The  fifth  meaning  is  also  foreign  to  our  present  purpose, 
and  besides  is  obsolete.  The  fourth  meaning  embodies 
only  a  special  form  of  illustration.  But  when  we  deal 
with  the  second  and  third  meanings,  we  come  to  close 
quarters  with  the  distinction  between  Exposition  and 
Illustration.  It  is  quite  obvious  that  if  we  set  some- 
thing in  a  clear  light,  or  exhibit  it  distinctly  or  conspicu- 
ously, we  are  really  doing  what  we  have  included  under 
the  head  of  demonstration  when  treating  of  Exposition. 
In  the  third  meaning  the  overlap  between  the  two 
processes  becomes  particularly  noticeable.  The  pur- 
pose of  Exposition  is  just  to  make  things  clear,  intel- 
ligible, or  apprehensible;  but  the  differentia  may  be 
found  hi  the  second  part,  "to  elucidate,  explain,  or  ex- 
emplify, as  by  means  of  figures,  comparisons,  and  ex- 
amples." Here  we  are  led  to  see  that  Illustration  is 
to  be  regarded  as  a  branch  of  Exposition.  A  mere 
setting  forth  of  principles  may  be  fairly  called  Expo- 
sition, but  could  not  be  justly  called  Illustration.  It 
is  only  when  we  proceed  to  supply  examples,  and  to 
institute  comparisons,  or  in  some  other  way  to  elabo- 
rate our  presentation,  that  we  can  be  said  to  illus- 
trate. 

The  secondary  meaning,  then,  of  Illustration,  as 
found  in  the  dictionary,  but  the  primary  meaning  for 
our  purposes,  may  be  said  to  be  the  process  of  throwing 
light  upon  something  that  is  assumed  to  be  known 
already  hi  a  vague  and  more  or  less  unsatisfactory  way. 
There  is  always  a  principle  or  body  of  principles  that 
may  be  regarded  as  given  (though  not,  perhaps,  neces- 


NATURE  AND  SCOPE  19 

sarily  given  to  the  pupil  at  the  beginning  of  the  illustra- 
tive process),  and  as  thus  forming  the  datum  of  the 
problem  of  Illustration.  This  I  should  like  the  reader 
to  permit  me  to  call  the  illustrandum  as  a  parallel  tech- 
nical term  to  the  expositandum.  One  part  of  the  func- 
tion of  Exposition  we  have  seen  is  to  present  new 
matter,  and  another  is  the  manipulation  of  matter  that 
has  been  already  presented.  One  is  tempted  to  limit 
Exposition  to  the  first  function  and  to  hand  over  all 
the  rest  to  Illustration.  Anything  that  we  do  or  say 
to  introduce  a  different  arrangement  of  ideas  already 
in  the  mind  of  the  pupil  would  on  this  view  be  properly 
called  Illustration.  We  are  not  to  lose  sight  of  the  fact 
that  Illustration  is  a  branch  of  Exposition,  and  must 
not  be  surprised  to  find  a  certain  overlapping  hi  respect 
of  the  matters  treated.  In  point  of  fact,  both  processes 
deal  with  both  the  new  and  the  old.  Yet  there  is  a 
difference  hi  then1  use  of  the  two  kinds  of  materials. 
The  new  ideas  introduced  by  Exposition  form  an  es- 
sential part  of  the  subject-matter  that  is  under  discus- 
sion, while  the  new  matter  introduced  by  way  of  Illus- 
tration may  have  only  a  secondary  connection  with 
the  subject-matter.  An  illustration  may  introduce 
new  ideas,  but  these  are  not  in  this  connection  treated 
as  of  importance  in  themselves,  but  only  as  throwing 
light  upon  the  ideas  that  are  at  the  time  being  ex- 
pounded. When  Mill  states  hi  his  second  canon  — 

"If  an  instance  in  which  the  phenomenon  under  investigation 
occurs,  and  an  instance  in  which  it  does  not  occur,  have  every 
circumstance  in  common  save  one,  that  one  occurring  only  in  the 
former,  the  circumstance  in  which  alone  the  two  instances  differ  is 
the  effect,  or  the  cause,  or  an  indispensable  part  of  the  cause,  of 
the  phenomenon  "  — 


20     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

he  is  expounding;    but  he  proceeds  to  illustrate  when 
he  goes  on  to  say:  — 

"If  A  BC,  A  DE,  A  FG  are  all  equally  followed  by  o,  then  a 
is  an  invariable  consequent  of  A.  If  a  b  c,  ade,  af  g  all  number 
A  among  their  antecedents,  then  A  is  connected  as  an  antecedent, 
by  some  invariable  law,  with  a." 1 

So  far  Mill  can  hardly  be  said  to  have  introduced  any 
new  ideas  by  way  of  illustration.  The  letters  are  mere 
pegs  ready  to  hang  matter  on  when  it  is  presented. 
When,  in  the  following  chapter  of  his  Logic,  he  intro- 
duces a  discussion  of  how  "arsenious  acid  and  the  salts 
of  lead,  bismuth,  copper,  and  mercury"  act  as  poisons, 
he  is  still  illustrating  the  canon,  but  he  is  introducing 
a  whole  series  of  entirely  fresh  ideas  that  have  no  con- 
nection in  themselves  with  the  subject-matter  under 
consideration,  which  is  the  logic  of  experimental  method. 
In  point  of  fact,  he  assumes  that  his  readers  know 
enough  about  chemistry  to  follow  easily  his  references 
to  Baron  Liebig's  theories.  As  a  general  rule  it  is 
unwise  to  use  as  illustrative  material  something  that  is 
very  unfamiliar  to  the  pupil.  It  is  seldom  good  policy 
to  use  many  new  ideas  in  an  illustration.  In  certain 
cases  it  may  be  justifiable  to  "work  up"  an  elaborate 
illustration  out  of  new  materials.  But  this  is  permis- 
sible only  when  it  is  possible  to  group  into  one  mass  a 
number  of  facts  that  are  useful  not  merely  as  illustra- 
tive of  certain  points,  but  as  themselves  important 
elements  in  the  organised  whole  that  makes  up  the 
subject  under  consideration.  Illustration  will  thus  be 
seen  to  be,  on  the  whole,  rather  a  work  of  arrange- 
ment than  of  addition. 

1  Logic,  Book  III,  Chap.  VIII. 


NATURE  AND  SCOPE  21 

All  the  same,  it  is  clear  that  illustrations  of  the  na- 
ture of  those  submitted  by  Mill  from  Baron  Liebig 
cannot  but  convey  in  passing  a  certain  amount  of  new 
information.  Not  only  do  they  make  clearer  and  more 
definite  the  points  that  they  illustrate,  but  they  in- 
crease the  mental  content  of  the  pupil.  He  may  not 
know  the  principle  of  the  lever  any  more  accurately 
after  a  long  series  of  illustrative  examples,  for  it  is 
quite  possible  to  understand  the  principle  from  only 
one  example,  but  he  will  understand  it  in  a  broader 
way.  His  experience  has  been  enriched  by  the  number 
of  cases  in  which  he  has  seen  the  principle  exemplified. 
He  does  not  know  it  more  accurately,  but  he  knows 
it  more  usefully. 

Hitherto  we  have  been  considering  Illustration 
merely  from  the  cognitive  side,  as  a  means  to  enable 
the  pupil  to  understand  something  that  is  difficult. 
But  our  object  is  not  always  to  make  another  under- 
stand something.  It  may  be  to  make  him  realise  more 
vividly,  to  appreciate,  to  enjoy.  We  must,  therefore, 
make  provision  for  the  aesthetic  use  of  Illustration. 
The  importance  of  this  aspect  must  not  be  underes- 
timated. An  old  clergyman,  addressing  an  audience 
of  beginners  in  his  own  profession,  told  them  that  they 
might  preach  over  and  over  the  same  sermon  at  rea- 
sonable intervals,  if  only  they  took  the  precaution  to 
change  the  text,  and  the  illustrations.1  The  congre- 
gation will  remember  the  illustrations  long  after  the 
expositions,  the  descriptions,  and  the  exhortations 

1  It  is  worth  noting  that  young  clergymen  have  complained  that 
this  gracious  permission  to  use  old  sermons  is  no  great  relief.  After 
all,  they  say,  it  is  the  illustrations  that  count,  and  if  one  has  to  work 
them  up  into  the  very  warp  and  woof  of  the  sermon,  this  practically 
means  that  the  sermon  has  to  be  rewritten. 


22     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

have  been  comfortably  forgotten.  Herein  lies  one  of 
the  chief  dangers  in  the  use  of  Illustration.  There  is  a 
strong  temptation  to  use  it  for  the  sake  of  its  own 
intrinsic  interest,  instead  of  for  the  interest  it  arouses 
in  connection  with  the  subject  under  discussion.  Un- 
less an  illustration  forms  part  of  the  very  nature  of  a 
lesson,  unless  it  is  worked  into  the  very  warp  and  woof 
of  the  whole,  it  is  illegitimate.1  An  illustration  must 
not  be  used  as  a  sedative.  Its  function  is  to  stimulate. 
The  teacher  may  think  that  he  is  entitled  to  introduce 
a  story  to  brighten  up  a  dull  lesson.  But  he  can  pur- 
chase this  privilege  only  by  inventing  a  connection 
between  the  story  and  the  lesson  he  is  teaching.  Some 
of  the  old  English  essayists  supply  capital  examples 
of  this  justifiable  combination  of  the  didactic  and  aes- 
thetic functions  of  Illustration.  Thomas  Fuller,  for  in- 
stance, makes  a  very  systematic  application  of  this 
form.  He  has  a  habit  of  marking  off  his  essays  into 
short  paragraphs,  each  beginning  with  an  easily  under- 
stood generalisation  immediately  followed  by  one  or 
more  illustrations  that  give  it  point.  Thus,  in  his  es- 
say, "Of  Memory,"  we  have  the  fourth  paragraph 
running :  - 

"  Overburthen  not  thy  memory  to  make  of  so  faithful  a  servant 
a  slave.  Remember,  Atlas  was  weary.  Have  as  much  reason  as  a 

1  People  who  make  a  study  of  the  art  of  advertising  take  the  view 
that  the  main  purpose  of  illustration  in  a  newspaper  or  on  a  poster 
is  to  attract  attention.  The  drawing  may  be  bad ;  it  may  not  accu- 
rately represent  the  object  advertised,  but  if  it  catches  the  attention 
of  the  passer-by  or  the  indifferent  newspaper  reader,  it  has  served  its 
purpose:  "Charles  Austin  Bates,  the  most  successful  advertisement 
designer  of  the  day,  has  repeatedly  asserted  that  the  function  of  the 
illustrator  is  to  attract  attention,  and  not  necessarily  to  illustrate." 
Illustrated  Advertising,  by  F.  W.  Johnston,  Ninth  Edition,  Toronto. 
1901.  (Introduction.) 


NATURE  AND  SCOPE  23 

camel,  to  rise  when  thou  hast  thy  full  load.  Memory,  like  a  purse, 
if  it  be  overfull  that  it  cannot  shut,  all  will  drop  out  of  it.  Take 
heed  of  a  gluttonous  curiosity  to  feed  on  many  things,  lest  the  greedi- 
ness of  the  appetite  of  thy  memory  spoil  the  digestion  thereof. 
Beza's  case  was  peculiar  and  memorable;  being  above  fourscore 
years  of  age,  he  perfectly  could  say  by  heart  any  Greek  chapter  in 
St.  Paul's  Epistles,  or  anything  else  which  he  had  learned  long  before, 
but  forgot  whatsoever  was  newly  told  him ;  his  memory,  like  an  inn, 
retaining  old  guests,  but  having  no  room  to  entertain  new." 

This  use  of  Illustration,  common  in  Bacon,  and  in  a 
less  condensed  form  in  modern  essayists,  is  valuable 
in  sermons  and  hortatory  addresses,  but  must  be  used 
sparingly  in  lectures,  and  more  sparingly  still  in  les- 
sons. 

Essayists  who  follow  more  or  less  the  method  of 
Fuller  are  read  largely  for  the  interest  of  the  illustra- 
tions. But,  after  all,  the  best  essayists  do  make  their 
generalisations  the  important  points.  All  the  rest  of 
the  matter  centres  round  them.  The  illustrations  may 
not  be  necessary  to  make  clear  the  actual  meaning  of 
the  thesis,  but  they  at  least  illustrate.  They  form  an 
organic  part  of  the  whole;  they  are  not  dragged  hi 
merely  for  the  sake  of  their  intrinsic  interest.  In  a  well- 
organised  lecture  or  lesson  it  is  possible  that  the  illus- 
trations may  occupy  more  space  than  the  statements 
to  be  illustrated;  but  the  main  statements  are  felt  to 
be  the  essential  matters;  the  illustrations,  however 
numerous,  are  organically  interstitial.  On  the  other 
hand,  there  are  lectures  and  lessons,  and  even  books, 
hi  which  the  illustrations  are  the  main  element,  and  the 
rest  of  the  matter  is  worked  in  around  them.  The 
generalisations  are  interstitial;  the  substantive  mat- 
ter is  made  up  of  what  are  nominally  illustrations. 
Lectures  on  "The  Humour  of  Mark  Twain,"  on  "The 


24      EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

Blunders  of  School  Children,"  on  "  Election  Time  in 
Texas,"  are  all  very  likely  to  turn  out  to  be  series  of 
illustrations  with  a  few  strenuously  invented  general- 
isations keeping  them  apart.  The  most  popular  form 
of  book  review  is  made-up  mainly  of  interstitial  matter, 
and  lantern  lectures  have  an  almost  irresistible  ten- 
dency to  resolve  themselves  into  interstitial  common- 
places that  only  a  good  set  of  slides  can  condone  in  the 
judgment  of  an  intelligent  audience. 

Some  teachers  may  reasonably  interpose  here,  and 
maintain  that  lantern  lectures  ought  to  be  interstitial. 
There  is  a  great  deal  to  be  said  in  favour  of  such  a  view. 
But  to  adopt  it  would  be  to  change  the  standpoint 
from  which  we  have  been  considering  the  whole  matter. 
It  is  quite  reasonable  to  maintain  that  the  most  valu- 
able part  of  a  lantern  lecture  is  not  what  the  lecturer 
says,  but  what  his  slides  show.  Still,  if  the  information 
conveyed  by  the  slides  is  regarded  as  the  primary 
matter,  they  can  no  longer  be  treated  as  illustrations: 
they  have  become  the  substantive  matter  of  teaching. 
The  interstitial  remarks  of  the  lecturer  are  really  illus- 
trative of  the  slides.  In  the  case  of  a  literary  lecture 
professing  to  give  a  critical  estimate  of  a  writer's  works, 
it  is  illegitimate  to  depend  for  the  main  interest  of  the 
lecture  on  the  intrinsic  attraction  of  the  quotations. 
The  interest  should  be  in  the  relation  the  lecturer  is 
able  to  establish  between  his  generalisations  and  the 
particular  quotations  that  he  uses  to  support  his  views. 
"Note  the  beauty  of  this  passage;"  "What  could  be 
more  inspiring  than  the  following;"  "If  you  wish  to 
know  what  pathos  means,  turn  with  me  to  the  Ode  to 
— ;"  "No  one  with  a  spark  of  humour  in  his  compo- 
sition could  refrain  from  chortling  over  the  exquisite 


NATURE  AND  SCOPE  25 

passage  I  am  about  to  read  to  you;"  all  these  are 
mere  bits  of  padding  that  mark  what  may  be  called 
finger-post  criticism.  On  the  other  hand,  some  of  the 
finest  passages  of  Shakespeare  may  be  read  with  almost 
no  interest  in  their  primary  meaning  because  they  are 
being  used  to  illustrate  a  point  in  the  Shakespeare- 
Bacon  controversy.  It  is  quite  possible  for  a  lantern 
lecture  to  depend  on  the  actual  lecture  that  is  delivered, 
so  that  the  hearers  recognise  that  the  slides,  however 
good  they  may  be,  would  either  have  been  meaning- 
less without  the  lecturer's  exposition,  or  would  have 
had  quite  a  different  meaning  from  that  they  actually 
took  under  his  manipulation. 

It  is  clearly  important  for  the  teacher  to  distinguish 
between  the  values  of  certain  materials  as  illustrations, 
on  the  one  hand,  and  as  the  subject  of  actual  teaching 
on  the  other.  Finger-post  criticism  has  its  place  in 
school.  Indeed,  it  is  probable  that  some  readers  of  this 
chapter  have  got  rather  angry  at  the  idea  of  spoiling 
Shakespeare  by  using  his  writings  merely  to  illustrate 
an  argument.  But  for  our  professional  purposes  it  is 
important  to  keep  apart  the  two  uses  of  subject-matter, 
the  one  as  illustration,  the  other  as  substantive  matter 
of  instruction.  It  is  an  excellent  thing  to  read  to  a  class 
a  series  of  extracts  from  a  standard  author  with  only 
a  few  explanatory  comments  —  probably  a  better  thing 
for  the  class  than  to  give  it  a  seriously  worked-out 
lecture  in  which  only  illustrative  extracts  are  given. 
We  have  to  remember  that  the  purpose  in  the  two  cases 
is  different.  In  the  first  we  are  giving  the  pupil  the 
actual  material;  in  the  second  we  are  entitled  to  as- 
sume that  the  pupil  has  the  material,  and  all  that  we 
have  to  do  is  to  manipulate  that  material  in  such  a  way 


26     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

as  to  enable  him  to  acquire  a  better  mastery  of  what 
he  already  possesses.  Under  ideal  conditions  in  a  lec- 
ture on  the  Humour  of  Tom  Hood  it  may  be  assumed 
that  the  audience  have  all  read  Hood's  works  at  least 
once.  The  lecturer  has  therefore  no  need  to  fall  back 
on  mere  finger-post  criticism;  and  on  the  other  hand, 
he  has  no  temptation  to  rely  upon  the  intrinsic  interest 
of  the  passages  he  quotes.  In  practice,  however,  it  is 
impossible  to  attain  the  ideal,  so  the  teacher  has  to 
combine  in  the  most  effective  way  he  can  the  two  uses 
of  his  material.  In  a  lesson  intended  to  deal  with  liter- 
ature as  subject-matter,  the  teacher  should  seek  to 
make  himself  as  little  prominent  as  possible.  The 
matter  is  the  important  thing.  So  long  as  lantern  slides 
are  used  as  teaching  matter  (docendum) ,  the  pupils  are 
entitled  to  attend  to  the  teacher's  explanations  only 
so  far  as  they  feel  the  need  of  them.  When  the  slides 
are  used  as  illustrations,  the  incidence  of  attention 
should  be  reversed. 

The  subject-matter  of  teaching  illustrations  is  of  con- 
siderable importance.  In  certain  branches  no  problem 
emerges.  Only  one  kind  of  illustration  is  possible,  and 
the  choice  of  the  best  material  in  that  kind  is  really  an 
essential  part  of  the  specialist's  knowledge  of  how  to 
teach  his  subject.  But  in  many  subjects  illustrations 
may  be  sought  from  all  parts  of  the  field  of  knowledge, 
and  the  question  arises  whether  it  is  better  to  select 
illustrations  from  matter  that  is  cognate  with  that 
the  pupils  are  dealing  with,  or  to  choose  matter  as 
different  from  that  as  possible.  Generally  speaking, 
it  is  better  to  keep  to  cognate  subjects,  as  in  this  way 
the  teacher  may  be  teaching  one  branch  substantively 
while  illustrating  another.  On  the  other  hand,  there 


NATURE  AND  SCOPE  27 

is  the  danger  of  weariness  if  the  pupils  are  never  allowed 
a  change  of  venue.  Teachers  are  beginning  to  realise, 
what  pupils  have  realised  some  time  ago,  that  it  is 
possible  to  carry  the  method  of  correlation  to  such  an 
extent  as  to  exhaust  all  possible  interest  in  certain 
matters.  Illustrating  in  a  circle  is  not  quite  so  deadly 
as  reasoning  in  a  circle,  but  it  has  its  serious  defects. 

From  what  has  gone  before,  it  might  appear  to  follow 
that  in  using  Illustration  we  must  always  adopt  the 
deductive  method.  The  illustrandum  is  given  as  a  sort 
of  general  statement,  which  the  rest  of  the  process 
works  out  and  applies,  as  in  ordinary  deduction.  But 
Illustration  may  sometimes  be  used  in  what  may  be 
fairly  called  an  inductive  way.  Indeed,  the  methods 
used  in  applying  Illustration  vary  between  two  ex- 
tremes. At  the  one  end  is  the  plan  of  depending 
mainly  upon  Exposition.  Everything  is  stated  in  the 
plainest  possible  terms,  and  illustrations  are  introduced 
only  where  absolutely  necessary,  and  are  always  stated 
to  be  illustrations.  They  are  formally  introduced  by 
as,  or  some  such  word,  or  are  actually  named  illustration 
or  example.  This  all  fits  in  with  the  deductive  notion. 
At  the  other  extreme  are  found  those  cases  where  the 
illustration  is  given  almost  without  comment,  and  its 
meaning  left  to  be  inferred.  Especially  when  many 
illustrations  are  given  and  the  pupil  is  led  to  draw  cer- 
tain inevitable  conclusions,  the  resemblance  to  induc- 
tion is  so  great  that  the  reader  may  not  unnaturally  say 
that  it  is  induction  and  nothing  else.  The  genders  of 
Latin  nouns,  as  gathered  from  inspection  of  their  mere 
form,  may  be  inculcated  by  a  series  of  exercises  to  our 
pupils  in  which  certain  typical  Latin  nouns  are  system- 
atically called  into  play  without  any  overt  reference 


28     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

to  their  gender.  But  some  may  be  inclined  to  question 
whether  this  is  really  Illustration.  Is  it  not  a  process 
in  which  we  teach  rather  than  merely  illustrate  ?  It  is 
true  that  the  illustrandum  does  not  appear  till  the 
process  is  completed,  but  it  has  been  in  the  teacher's 
mind  throughout.  It  may  not,  therefore,  be  altogether 
unreasonable  to  regard  the  process  as  one  of  Illustra- 
tion, the  teacher  adopting  the  deductive  attitude  and 
passing  from  the  generalisation  to  the  particulars,  and 
the  pupils  reversing  this  order.  This  view  is  worth 
elaborating  a  little,  as  it  is  not  quite  in  harmony 
with  the  usual  nomenclature. 

Sometimes,  in  ordinary  experience,  light  is  thrown 
upon  some  matter  that  nevertheless  cannot  be  called 
the  illustrandum,  since,  at  the  beginning,  it  is  not  pres- 
ent as  such  in  the  mind  of  either  the  pupil  or  the 
teacher.  A  person  who  knew  no  German  was  called 
upon  to  make  a  vocabulary  that  included  over  two 
thousand  German  nouns.  She  had  to  indicate  in  each 
case  the  gender,  the  genitive,  and  the  meaning  of  the 
noun.  Her  method  was  the  straightforward  one  of 
looking  up  each  word  in  a  standard  German  dictionary, 
and  copying  out  the  relevant  details.  As  the  work 
progressed,  she  found  that  she  could  anticipate  with 
increasing  accuracy  the  gender  and  genitive  of  each 
new  noun  as  it  presented  itself;  till  towards  the  end 
she  was  strongly  tempted  to  depend  upon  her  general 
impression,  without  troubling  to  verify  it  by  reference 
to  the  dictionary. 

A  still  more  striking  case  is  one  that  occurred  under 
the  deplorably  bad  system  of  payment  by  results,  that 
used  to  obtain  hi  England,  in  which  the  teacher's  pro- 
fessional reputation  depended  upon  the  percentage  of 


NATURE  AND  SCOPE  29 

pupils  he  could  contrive  to  squeeze  through  certain 
individual  examination  tests  at  the  end  of  each  school 
year.  A  harassed  teacher,  who  had  not  enough  tune  to 
attend  to  the  dullards  that  under  this  system  were  the 
persons  of  chief  importance,  tried  to  get  rid  of  the 
troublesome  clever  pupils  in  her  youngest  class  by  keep- 
ing them  busy  with  long  addition  sums,  while  she  de- 
voted all  her  energy  to  getting  her  dullards  to  work 
little  sums  with  sufficient  accuracy  to  obtain  the  coveted 
pass.  Through  much  practice  the  clever  pupils  were 
able  to  work  the  long  sums  so  rapidly  that  they  were 
continually  worrying  the  poor  teacher  by  coming  back 
for  more.  To  save  time  in  giving  out  fresh  sums,  she 
dictated  only  one  line,  say  987,526,  and  told  the  pupils 
to  repeat  that  line  on  their  slates  another  eight  times, 
making  nine  lines  in  all,  and  then  add  the  whole.  The 
remarkable  thing  was  that  after  some  weeks  of  this  in- 
genious labour-saving  device,  the  poor  teacher  was  more 
harassed  than  ever.  The  children  appeared  to  have 
acquired  a  positively  uncanny  speed  in  addition.  On 
investigation  it  was  found  that  the  pupils  had  gradually 
noticed  that  there  was  something  peculiarly  sym- 
metrical about  the  new  sums  the  teacher  was  giving 
them.  Some  of  the  more  intelligent  among  them  began 
to  see  that  it  was  a  pity  to  waste  time  adding  up  a 
column  of  nine  eights  when  they  had  added  up  such  a 
column  a  little  while  ago.  They  began,  therefore,  to 
keep  a  note  of  results  for  future  use,  and  gradually 
gave  up  adding  at  all,  except  in  the  matter  of  carrying 
from  one  column  to  another.  The  step  from  this  to 
pure  multiplication  was  easy,  but  as  a  matter  of  fact 
was  not  made  by  the  pupils  themselves;  the  secret  of 
multiplication  was  communicated  to  them  (for  a  con- 


30     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

sideration)  by  certain  pupils  in  higher  classes  to  whom 
the  young  experimenters  had  been  talking  about  the 
peculiar  sums  they  had  lately  been  having.  The  net 
result  was  that  those  pupils  learnt  in  a  few  weeks,  and 
with  great  satisfaction,  the  full  meaning  of  the  multi- 
plication table  and  its  application,  matters  that  under 
ordinary  circumstances  take  a  whole  school  year  to 
master. 

It  might  be  argued  that  in  these  two  cases  the 
pupil  passed  from  the  illustration  to  the  illustran- 
dum.  But  this  is  an  unnecessary  strain  on  the  terms. 
It  is  better  to  restrict  the  term  Illustration  to  those  cases 
in  which  there  is  a  deliberate  attempt  to  throw  light 
upon  a  given  subject.  Here,  to  be  sure,  light  was 
thrown  upon  certain  matters,  but  without  any  delib- 
erate intention  on  the  part  of  either  teacher  or  pupil. 
The  learning,  in  fact,  was  carried  on  in  the  ordinary 
inductive  way. 

The  case  is  somewhat  different  when  the  teacher 
makes  a  deliberate  use  of  the  illustration  before  pre- 
senting the  illustrandum.  He  is  often  able  to  arrange 
matters  so  that  certain  experiences  of  school  difficulties 
that  must  occur  at  any  rate  among  his  pupils  shall 
occur  at  certain  stages  that  are  convenient  for  him. 
He  can,  in  short,  modify  the  order  of  the  development 
of  the  pupil's  mental  experience  in  such  a  way  that  the 
elements  of  this  experience  shall  form  certain  combi- 
nations that  from  the  point  of  view  of  the  school  are 
desirable  because  they  lead  to  the  pupil's  coming  to 
certain  desired  conclusions.  To  put  it  somewhat  less 
abstractly,  it  is  quite  possible  for  a  master  who  has 
taught  the  same  school  grade  for  several  years  to  know 
very  exactly  how  certain  of  the  special  points  to  be 


NATURE  AND  SCOPE  31 

dealt  with  in  that  grade  will  affect  certain  minds. 
He  is  therefore  in  a  position  to  arrange  the  matters  to 
be  presented  in  the  order  he  thinks  will  best  aid  their 
proper  assimilation.  For  example,  the  construction 
of  the  accusative  with  the  infinitive  in  Latin  involves 
problems  for  the  young  mind  that  are  insoluble  at  cer- 
tain stages  of  knowledge.  This  subject  may  be  illus- 
trated in  advance  by  a  carefully  arranged  series  of 
lessons  that  have  no  apparent  connection  with  the 
oratio  obliqua,  as  found  in  Latin.  English  grammar 
may  be  so  taught  as  to  pave  the  way,  and  even  the  use 
of  brackets  in  algebra  may  be  regarded  as  a  prepara- 
tion, —  as  may  be  seen  hi  the  interesting  little  mono- 
graph on  the  subject  by  the  Rev.  J.  H.  Raven.1 

In  the  ordinary  sense  of  the  term  an  illustration  is 
expected  to  accompany  the  subject-matter  to  be  illus- 
trated, so  it  must  be  admitted  to  be  a  little  strain  on 
the  term  to  call  such  processes  as  those  we  have  dealt 
with  in  the  last  paragraph  Anticipatory  Illustration. 
To  be  sure,  the  teacher  always  has  the  illustrandum 
before  him  as  he  prepares  the  exercises  that  are  to  throw 
light  upon  difficulties  that  have  not  yet  arisen  in  the 
pupil's  mind,  and  this  gives  a  certain  amount  of  justi- 
fication for  the  introduction  of  the  term  Anticipatory 

1  "  Do  the  two  accusatives  both  feel  the  influence  of  the  Transitive 
didt,  and  so  form  a  complex  noun,  governed  by  didt,  so  that  the 
analysis  will  be:  He  mentions  the-enemy's-coming  f  Key  (Lot.  Gram., 
§  911)  seems  to  take  a  somewhat  similar  view  to  this.  In  analysing 
Ferunt  Cassarem  rediisse,  he  has  this  original  note :  '  A  mathematician 
might  have  expressed  this  by  —  Ferunt  (Ccesar  rediit)em,  attaching 
the  symbol  of  the  accusative  case  to  the  clause.  As  the  Romans 
were  afraid  to  do  this,  adopting  what  under  the  circumstances  was 
perhaps  the  best  makeshift,  they  selected  for  the  addition  of  the 
suffix  the  chief  substantive.'"  —  Latin  Exercises  in  the  Oratio  Obliqua, 
by  the  Rev.  J.  H.  Raven,  p.  55. 


32     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

Illustration.  But  the  real  reason  for  seeking  to  use 
the  phrase  is  that  there  is  need  for  some  term  to  desig- 
nate a  process  whose  importance  is  now  beginning  to  be 
appreciated  in  schools.  Using  Anticipatory  Illustra- 
tion in  such  a  way  that  pupils  must  reach  certain  gener- 
alisations, may  be  regarded  as  a  form  of  inductive  teach- 
ing. The  pupil  may  be  so  fed  with  illustrative  matter 
that  he  is  practically  coerced  into  reaching  certain  con- 
clusions. The  heuristic  method,  in  its  healthier  forms, 
is  nothing  more  than  a  system  of  Anticipatory  Illus- 
tration inevitably  leading  to  a  conclusion  that  already 
exists  in  the  teacher's  mind.  It  is  a  caricature  of  the 
method  to  describe  it  as  a  process  of  placing  the  pupils 
in  the  position  of  the  original  discoverer  of  a  certain 
truth,  and  keeping  them  there  till  they  discover  it  for 
themselves.  We  cannot  put  pupils  in  the  position  of 
the  original  discoverer.  We  can  turn  them  loose  in  an 
orchard  and  let  them  watch  the  apples  falling;  but  it 
would  be  difficult  to  say  how  much  time  we  should  give 
them  before  we  come  back  to  find  them  in  possession 
of  the  theory  of  gravitation.  The  teacher  on  the  heu- 
ristic method  never  lets  go  the  guiding  reins.  He  may 
hold  them  now  loose  and  now  tight,  but  he  never  drops 
them.  He  knows  the  course  and  he  keeps  his  pupils 
in  it  —  with  the  minimum  amount  of  restraint,  it  is 
true,  but  the  restraint  is  none  the  less  real.  It  is, 
throughout,  a  system  of  Anticipatory  Illustration. 

It  is  sometimes  maintained  that  the  heuristic  method 
gives  no  real  training  in  induction,  since  all  the  matter 
is  so  carefully  arranged  beforehand  that  the  mind  is 
not  left  free.  But  the  mind,  as  a  matter  of  fact,  is, 
under  no  circumstances,  ever  left  free.  It  must  react 
upon  what  is  presented  to  it,  and  it  acts  in  the  same 


NATURE  AND  SCOPE  33 

way  upon  the  material  presented,  whether  that  comes 
at  haphazard  or  is  carefully  arranged  in  a  definite  order. 
The  induction  a  pupil  makes  as  the  result  of  considering 
a  number  of  anticipatory  illustrations  is  as  genuine  as 
one  that  he  makes  in  his  ordinary  experience.  The 
fact  that  his  ordinary  induction  is  so  often  wrong, 
because  the  matter  is  not  presented  in  a  helpful  order, 
is  surely  no  advantage.  So  far  as  the  intellectual  pro- 
cess is  concerned,  there  is  no  difference  in  the  two  cases. 
An  induction  either  is  an  induction  or  it  is  not. 

A  more  plausible  objection  is  that  Anticipatory  Illus- 
tration may  be  so  arranged  as  to  prevent  the  possibil- 
ity of  error,  and  thus  deprive  the  pupil  of  that  prac- 
tice in  dealing  with  deceptive  cases  that  is  so  necessary 
as  a  preparation  for  the  work  of  life.  But  here  it  is 
only  necessary  to  remark  that,  in  spite  of  the  teacher's 
best  endeavours,  he  will  find  it  almost  impossible  to  ar- 
range his  anticipatory  illustrations  so  that  there  is  no 
loophole  for  error.  Further,  at  later  stages,  the  pupil 
is  left  more  and  more  to  his  own  resources.  Under  any 
system  inductions  must  be  verified,  and  this  verifica- 
tion may  be  as  well  taught  in  connection  with  the 
heuristic  method  as  with  any  other.  All  the  needful 
precautions  can  be  applied  here  as  elsewhere. 

As  an  example  of  the  application  of  Anticipatory 
Illustration  with  the  minimum  possibility  of  error, 
take  the  case  of  teaching  Euler's  Theorem,  that  gives 
the  formulae  for  the  number  of  faces,  corners,  and  edges 
of  a  pyramid  or  prism  having  a  given  geometrical  figure 
as  base.  The  data  of  the  theorem  may  be  so  presented 
that  the  pupils  must  discover  it  for  themselves.  They 
are  assumed  to  know  what  is  meant  by  a  face,  a  cor- 
ner and  an  edge.  The  teacher  supplies  the  pupils  with 


EXPOSITION   AND   ILLUSTRATION   IN  TEACHING 


the  sixteen  solids  named  in  the  following  table,  but  the 
numbers  as  they  appear  on  the  printed  table  are  not 
inserted :  — 

EULER'S  THEOREM 


PYRAMIDS 

PRISMS 

XT         v    /•*«   Qrv 

Faces 

Corners 

Edges 

Faces 

Corners 

Edges 

4 

4 

6 

Triangular 

5 

6 

9 

5 

5 

8 

Square 

6 

8 

12 

6 

6 

10 

Pentagonal 

7 

10 

15 

7 

7 

12 

Hexagonal 

8 

12 

18 

8 

8 

14 

Heptagonal 

9 

14 

21 

9 

9 

16 

Octagonal 

10 

16 

24 

10 

10 

18 

Nonagonal 

11 

18 

27 

11 

11 

20 

Decagonal 

12. 

20 

30 

n  +1 

n  +  1 

2n 

n-gonal 

n  +2 

2n 

3n 

Provided  with  this  blank  table  and  the  necessary 
solids,  the  pupil  is  called  upon  to  fill  in  the  required 
numbers  by  the  simple  process  of  counting  from  the 
actual  solids  the  number  of  faces,  corners,  and  edges. 
All  he  is  asked  to  do  is  to  fill  up  the  table  as  far  as  the 
decagonal  solids.  Naturally  the  generalised  expres- 
sions in  terms  of  n  that  occur  at  the  end  of  the  table 
are  not  even  suggested  to  the  pupil.  It  is  the  purpose 
of  the  lesson  to  lead  the  pupils  to  reach  the  generalisa- 
tions in  n  for  themselves.  To  enunciate  these  at  the 
beginning  of  the  lesson  would  be  what  Professor  Henry 
E.  Armstrong  calls  "criminal."  * 

At  first  the  pupils  fill  up  the  table  in  that  conscien- 
tiously indifferent  way  that  children  have  of  dealing 
with  easy  routine  exercises.  By  and  by  they  begin  to 

1  The  Teaching  of  Scientific  Method,  p.  254, 


NATURE  AND   SCOPE  35 

note  a  certain  symmetry,  and  their  intellectual  interest 
is  aroused.  It  is  an  excellent  plan  to  omit  two  of  the 
figures,  say  the  octagonal  pyramid  and  the  nonagonal 
prism,  and  invite  the  pupils  to  fill  up  the  corresponding 
spaces  by  calculation.  It  will  be  found  that  fully  half 
of  the  class  will  be  able  to  do  this  directly  they  come 
to  the  place  of  the  missing  figure,  and  almost  all  the 
rest  of  the  class  will  be  able  to  fill  in  the  blanks  after 
they  have  completed  the  entries  so  far  as  they  have 
solid  figures  to  count  from. 

The  second  stage  consists  in  requiring  the  pupils  to 
continue  the  table,  filling  in  the  non-technical  terms 
in  the  name  column,  11-gonal,  12-gonal,  13-gonal, 
and  so  forth  down  to  20-gonal.  Experience  showed 
that  almost  every  pupil  in  a  class  of  sixty  boys  of  ten 
years  of  age  could  complete  the  table  up  to  20,  and  all 
this  without  one  single  word  of  explanation  from  the 
time  the  first  number  was  set  down  till  the  60  edges  of 
the  20-gonal  prism  were  recorded. 

Keeping  to  the  case  of  the  class  just  mentioned, 
the  third  stage  consisted  in  setting  the  pupils  to  fill  up 
the  figures  for  a  40-gonal  figure,  then  for  a  60-gonal, 
then  for  a  100-gonal  solid.  Here  there  was  a  bigger 
percentage  of  breakdowns,  and  the  method  adopted  was 
to  write  the  correct  line  of  figures  on  the  blackboard 
after  each  solid  had  been  attempted.  In  this  way 
those  who  failed  in  the  40  solid  saw  how  things 
went,  and  generally  succeeded  with  the  60  or  the 
100  solid. 

The  fourth  stage  consisted  in  a  series  of  exercises 
such  as :  How  many  edges  has  a  45-gonal  pyramid  ? 
a  45-gonal  prism  ?  How  many  corners  has  a  72-gonal 
prism  ?  The  correct  answer  was  in  each  case  placed 


36     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

upon  the  board,  and  the  pupils  were  thus  enabled  to 
correct  any  miscalculation. 

The  fifth  stage  consisted  in  exercises  that  worked 
backwards:  A  ?-gonal  solid  pyramid  has  41  corners  ; 
how  many  faces  has  it  ?  How  many  edges  ?  What 
-gonal  is  it  ?  (That  is,  what  number  should  go  before 
the  -gonal  in  the  name  column  ?) 

The  final  stage  consisted  in  an  invitation  to  fill  up 
the  n-gonal  figures.  All  that  was  explained  was  that 
n  stood  for  any  number,  and  that  what  was  to  be  noted 
was  whether  the  different  numbers  would  be  greater  or 
less  than  n,  and  by  how  much.  At  the  first  exercise 
thirty-five  boys  wrote  down  the  correct  generalised 
form.  They  had  won  their  generalisation. 


CHAPTER  II 
MENTAL  CONTENT 

TEACHEES  are  now  familiar  with  the  phenomena  of 
apperception.  At  the  earliest  stages  pure  sensation  is 
possible  to  the  developing  human  being,  but  very  soon 
sensations  are  associated  with  meaning  and  become 
perceptions.  Thereafter  every  stimulus  that  the  mind 
has  to  deal  with  is  modified  by  the  results  of  previous 
stimulations.  When  we  reach  the  plane  of  ideas,  it  is 
found  that  while  every  new  idea  presented  is  acted  upon 
in  accordance  with  the  laws  of  mind,  these  laws  can 
only  be  applied  as  conditioned  by  the  other  ideas  at 
that  time  possessed  by  the  mind.  In  other  words,  each 
new  idea  is  acted  upon  by  all  the  other  ideas  at  that  time 
available  in  the  mind  in  question.  This  process  is 
known  as  apperception.  A  given  mind  possessed  of 
certain  ideas  must  react  in  a  determinate  way  when  a 
given  new  idea  is  presented  to  it.  Any  one  therefore 
who  knows  the  general  laws  of  mental  activity  and  the 
content  of  a  given  mind  may  act  upon  that  mind  with 
a  fair  chance  of  being  able  to  produce  a  desired  mental 
result.  In  point  of  fact  this  is  what  the  expositor  does, 
for  Exposition  may  be  regarded  as  the  process  of  guid- 
ing and  directing  apperception  in  another  mind. 

The  first  assumption,  then,  underlying  the  art  of 
Exposition  is  that  it  is  possible  for  one  mind  to  act 
upon  another.  Successful  exposition  implies  that  one 

37 


38     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

mind  has  been  able  to  produce  a  predetermined  effect 
upon  another.  Now  while  our  ordinary  experience 
leads  us  to  believe  that  this  interaction  between  minds 
is  continually  going  on,  the  slightest  dip  beneath  the 
surface  shows  us  that  the  matter  is  not  nearly  so  simple 
as  it  appears.  There  is  no  direct  communication 
between  minds.  Mind  understands  mind  only  by 
an  elaborate  system  of  interpretation.  Philosophers 
puzzle  themselves  and  their  readers  over  the  problem  of 
the  relation  between  the  individual  consciousness  and 
what  they  call  the  general  consciousness.  But  what- 
ever this  relation  may  be  it  is  one  that  does  not  admit 
of  articulate  expression.  For  all  practical  purposes 
each  individual  consciousness  is  insulated  from  every 
other.  Consciousness  is  as  impenetrable  as  matter: 
by  no  possibility  can  we  penetrate  into  the  conscious- 
ness of  another.  What  goes  on  in  that  other  conscious- 
ness can  be  understood  by  us  only  as  the  result  of  a 
process  of  inference  from  our  own  experience.  The 
everyday  act  of  influencing  the  mind  of  another,  there- 
fore, acquires  all  the  interest  of  a  mystery. 

We  may  never  be  able  to  explain  fully  all  that  under- 
lies this  mystery,  but  we  can  at  least  lay  down  certain 
conditions  that  must  be  complied  with  if  we  are  to 
succeed  in  producing  upon  the  mind  of  another  a  pre- 
determined effect.  To  begin  with,  we  must  be  able  to 
catch  and  retain  the  attention  of  the  pupil.  Next 
we  have  to  acquire  the  power  of  manipulating  his  men- 
tal content  so  that  there  shall  arise  in  his  mind  a  com- 
bination of  elements  similar  to  a  certain  combination 
already  existing  in  our  own  mind.  To  do  this  we  must 
have  a  knowledge  of  the  mental  content  of  the  pupil. 
The  next  condition  of  successful  exposition  is  a  knowl- 


MENTAL  CONTENT  39 

edge  of  the  laws  according  to  which  mind  in  general 
acts.     No  doubt  there  are  great  varieties  in  the  de- 
tailed working  of  individual  minds,  but  there  are  cer- 
tain laws  which  are  of  a  very  general  character,  it  is 
true,  but  which  within  the  wide  limits  of  their  applica- 
tion are  absolute.     We  cannot  break  these  laws  even 
if  we  try;   it  is  according  to  these  laws  that  the  mind 
always  reacts  upon  material  presented  to  it.    They 
are  generally  known  as  the  Laws  of  Thought  as  Thought, 
and  are  more  frequently  found  in  books  on  Logic  than 
in  books  on  Psychology.     So  exceedingly  general  are 
they,  that  when  they  are  stated,  they  sound  particularly 
empty.     But  it  has  to  be  remembered  that  their  empti- 
ness is  the  result  of  their  universality.     They  run  as 
follows:   The  first,  known  as  the  Law  of    Identity, 
is  represented  by  the  enlightening  formula  A  is  A. 
This  again  is  explained  to  mean  that  everything  is 
equal  to  itself,  or  the  whole  is  equal  to  the  sum  of  the 
parts.     It  has  to  be  noted  that  this  statement  has  noth- 
ing to  do  with  either  the  whole  or  the  parts,  except  in 
their  relations  as  whole  and  parts.     It  is  found  to  be 
an  imperative  law  of  our  thinking  that  we  shall,  under 
no   circumstances   whatever,    conceive   the  whole   as 
being  either  more  or  less  than  the  sum  of  the  parts. 
Of  the  many  meanings  that  have  been  given  to  the 
Principle  of  Identity  perhaps  the  one  most  in  point  here 
is  that  supported  by  F.  H.  Bradley.     This  is  that  under 
identical  circumstances  the  mind  must  reaffirm  what 
it  has  once  affirmed.     For  example,  if  I  have  once  truly 
said  that  the  sky  is  blue,  I  am  bound  to  maintain  the 
affirmation,  even  though  the  sky,  as  a  matter  of  fact,  is 
blue  no  longer.     "Once  true,  always  true;  once  false, 
always  false."  1 

1  The  Principles  of  Logic,  p.  133. 


40    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

The  Law  of  Non-contradiction  is  the  second  of  these 
momentous  laws.  This  is  expressed  in  the  formula: 
What  is  contradictory  is  unthinkable.  Its  shortened 
form  is  A  =  not-A  =  0,  or  A  —  A  =  0.  To  take  a 
concrete  case,  a  watch  cannot  be  both  correct  and  in- 
correct at  the  same  moment,  and  tested  by  the  same 
standard.  A  person  cannot  be  at  the  same  tune  guilty 
and  not  guilty. 

The  third  law  introduces  us  to  what  is  known  as  the 
Excluded  Third,  or  the  Excluded  Middle.  This  com- 
pels us  to  think  that  of  two  repugnant  notions  that  can- 
not both  coexist,  one  or  the  other  does  exist.  "Of 
contradictory  attributions  we  can  only  affirm  one  of  a 
thing;  and  if  one  be  explicitly  affirmed,  the  other  is 
implicitly  denied.  A  either  is  or  is  not.  A  either  is  or 
is  not  B."  l  A  centaur  either  is  or  is  not.  Socrates 
either  is  or  is  not  guilty. 

From  our  present  point  of  view  the  fourth  law  is  of 
less  consequence  than  the  others.  It  is  known  as  the 
Law  of  Sufficient  Reason,  and  limits  itself  to  the  asser- 
tion that  we  must  infer  nothing  without  a  cause,  or 
rather  without  a  ground  or  reason,  as  cause  is  usually 
restricted  to  the  region  of  the  actual,  and  reason  to  that 
of  thought.  The  very  statement  of  this  distinction  is 
an  explanation  of  the  comparative  unimportance  of 
this  law  as  illustrating  the  ultimate  process  of  thought. 
The  nature  and  origin  of  the  idea  of  causation  has  been 
elaborately  discussed,  and  when  so  much  can  be  said 
in  favour  of  the  Associational  origin  of  the  idea  of  Causa- 
tion, it  cannot  be  maintained  that  this  law  has  the  cer- 
tainty that  marks  the  others. 

So  unassailable  are  these  three  laws  that  the  general 

1  Sir  William  Hamilton:   Lectures,  Vol.  Ill,  p.  83. 


MENTAL  CONTENT  41 

feeling  of  every  one  who  hears  them  for  the  first  time 
is  that  they  are  superfluous,  if  not  indeed  a  little  silly. 
Why  state  them  so  ponderously  when  no  one  questions 
their  truth.  Are  we  any  further  forward  when  we  have 
admitted  that  A  is  A,  that  A  cannot  be  both  A  and  not 
A,  that  a  thing  must  be  either  A  or  not  A?  Yet  it  is 
because  of  our  unanimity  on  these  apparently  unim- 
portant points  that  we  are  able  to  reason  with  one 
another  in  the  full  assurance  that  we  shall  come  to 
certain  inevitable  conclusions,  if  only  the  facts  are 
stated  aright.  Two  minds  that  are  given  the  same  facts 
cannot  but  come  to  the  same  conclusion.  Depending 
upon  these  laws,  we  are  able  to  rely  upon  producing  by 
our  exposition  a  definite  calculable  effect  upon  the 
minds  of  others.  Given  certain  facts,  we  can  prophesy 
the  mind's  reaction  upon  them. 

Unfortunately  the  certainty  of  reaction  is  disturbed 
by  the  nature  of  the  facts  submitted  to  the  mind. 
When  dealing  with  quite  abstract  elements,  as  in  formal 
logic  and  pure  mathematics,  the  action  of  the  mind 
can  be  depended  upon.  But  unfortunately  the  greater 
part  of  our  mental  activity  is  carried  on  in  connection 
with  matters  that  are  far  from  abstract.  It  is  custom- 
ary to  use  a  figure  of  speech  and  speak,  as  we  have  done 
once  or  twice  already,  of  mental  content.  Naturally 
we  must  be  on  our  guard  against  accepting  this  figure 
as  expressing  literal  truth.  The  relation  between  the 
mind  and  mental  content  is  not  that  between  container 
and  thing  contained.  For  convenience  of  expression 
we  speak  of  the  mind  and  the  subject  upon  which  the 
mind  acts,  but  the  two  terms  are  often  very  loosely 
understood.  Occasionally  we  think  about  this  subject 
as  something  outside  of  us  altogether.  For  example, 


42     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

the  mind  may  be  said  to  act  upon  the  colours  when  we 
watch  a  sunset.  If  this  be  so,  the  mind  is  acting  upon 
something  that  is  material.  But  it  would  be  better 
to  say  that  the  brain  through  the  medium  of  the  sense 
organs  is  being  affected  in  a  certain  way,  and  that  as 
a  result  the  mind  is  stirred  to  a  particular  kind  of  ac- 
tivity. The  fundamental  connection  between  mind 
and  matter  is  fortunately  no  part  of  our  present  busi- 
ness; what  we  are  interested  in  is  the  connection  be- 
tween the  mind  and  that  upon  which  the  mind  acts. 
Speaking  generally,  the  mind  is  said  to  act  upon  ideas.1 
Mental  content  is  usually  regarded  as  being  made  up  of 
ideas.  It  is  a  very  convenient  way  of  expressing  our- 
selves to  speak  of  the  mind  as  a  sort  of  force  that  acts 
upon  certain  entities  called  ideas.  But  ideas  are  not 
things  from  without  that  the  mind  takes  into  itself 
and  builds  up  into  useful  combinations.  Still  less  are 
they  independent  entities  that  act  on  their  own  initia- 
tive. Ideas  are  not  so  much  things  as  forces.  They 
are  modes  in  which  the  mind  manifests  its  activity. 
It  is  not  so  much  that  the  mind  has  ideas  as  that  the 
mind  is  ideas.  It  was  formerly  fashionable  to  speak 
of  the  mind  as  having  a  certain  number  of  faculties; 
but  recent  writers  regard  the  faculties  as  merely  dif- 
ferent ways  in  which  the  mind  shows  its  activity: 
they  are  sometimes  spoken  of  as  modes  of  being  con- 
scious.2 This  description  might  be  equally  applied  to 
ideas,  the  difference  being  that  the  ideas  are  modes 
of  consciousness  more  specialised  than  are  the  facul- 

1  Cf.  Locke's  definition  of  an  idea  as  "whatsoever  is  the  object  of 
the  understanding  when  a  man  thinks."  Human  Understanding, 
Bk.  I,  Chap.  1,  §8. 

*  Cf .  Professor  Stout :  Manual  of  Psychology,  Book  I,  Chap.  I. 


MENTAL  CONTENT  43 

ties.  My  idea  of  a  table  is  my  mode  of  being  conscious 
of  tables,  but  it  has  its  peculiarities.  My  experience 
of  tables  has  not  been  exactly  the  same  as  everybody 
else's,  and  my  mode  of  being  conscious  of  a  table  is 
affected  accordingly. 

We  must  not  be  led  into  supposing  that  ideas  always 
represent  definite  separate  units  such  as  we  call  things, 
or  even  that  they  always  correspond  to  what  are  called 
the  substantive  elements  of  thought.  It  is  found  that 
the  elements  of  thought  may  be  roughly  arranged  into 
two  classes :  those  upon  which  the  mind  may  rest  for 
at  least  a  brief  tune,  and  those  that  are  always  on  the 
wing  and  cannot  be  made  by  themselves  the  matter 
of  thought,  but  must  always  be  considered  in  relation 
to  other  thought-elements.  The  first  class  are  called 
the  substantive,  the  second  the  transitive,  elements. 
Naturally  these  terms  are  not  to  be  confounded  with 
their  equivalents  in  grammar.  For  the  purposes  of 
Psychology,  for  example,  a  verb  may  be  regarded  as  a 
substantive.  The  mind  can  rest  on  the  idea  implied 
in  the  verb  to  walk,  but  it  cannot  deal  with  such  a  word 
as  of  unless  it  gets  the  help  of  other  ideas.  The  dis- 
tinction between  the  substantive  and  transitive  must 
not  be  pushed  too  far.  We  can  in  thought  isolate  tran- 
sitive ideas  and  —  with  the  help  of  other  thought-ele- 
ments —  deal  with  them  as  substantives.  Have  we 
not  erudite  notes  on  such  transitive  elements  as  are 
indicated  by  pev  and  Be  ?  There  is,  in  fact,  always  a 
strong  tendency  to  turn  the  transitive  elements  into 
substantive.  We  are  disinclined  to  let  an  idea  act 
merely  as  a  force.  We  want  to  pause  over  it,  and  wher- 
ever possible,  analyse  it.  In  actual  experience,  how- 
ever, we  frequently  fail  to  separate  out  the  definite 


44     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

meaning  of  a  word  (which,  of  course,  represents  an  idea), 
and  yet  we  can  use  it  quite  accurately.  We  often  find 
a  difficulty  in  explaining  the  meaning  of  a  peculiar  turn 
in  the  mother  tongue.  We  know  that  the  expression  is 
correct,  and  that  it  is  the  only  expression  that  will 
meet  the  case,  and  yet  we  cannot  explain  to  the  en- 
quiring foreigner  why.  What  is  called  the  Sprachgefuhl 
represents  this  general  sense  of  the  value  of  certain  of  the 
transitive  elements  of  thought.  We  recognise  them  as 
forces,  though  we  are  not  always  able  to  control  them. 
The  uneasiness  we  experience  in  dealing  with  the  tran- 
sitive elements  of  thought  results  from  a  natural  ten- 
dency we  all  have  to  endow  abstractions  with  a  more 
or  less  independent  objective  existence.  There  is,  hi 
fact,  in  the  human  mind  a  strong  bias  toward  the 
"Thing"  stage,  and  this  bias  must  be  allowed  for  in 
our  efforts  to  convey  thoughts  from  mind  to  mind. 
The  fundamental  tendency  of  the  human  mind  to  treat 
thoughts  as  things  is  illustrated  in  the  universal  bias 
toward  personifying  the  forces  of  nature.  Poets  spend 
a  good  deal  of  their  time  in  this  process  of  giving  to 
airy  nothings  a  local  habitation  and  a  name.  But 
hypostasis,  as  this  tendency  to  reify  thoughts  is  called, 
is  apt  to  induce  confusion.  It  leads  us  to  imagine, 
for  example,  that  because  we  can  remember  and  imag- 
ine and  judge  we  must  have  faculties  of  memory, 
imagination,  and  judgment.  A  clock  can  tick,  but  no 
one  thinks  of  endowing  it  with  the  faculty  of  tickibility. 
Yet  if  we  had  occasion  to  speak  a  great  deal  about  a 
clock's  power  of  ticking,  we  would  almost  certainly  fall 
into  speaking  of  its  tickibility  or  its  tickipacity.  For 
expository  purposes  it  is  necessary  to  have  a  term  to 
describe  the  various  modes  of  being  conscious,  and  so 


MENTAL  CONTENT  45 

long  as  we  do  not  imagine  that  there  is  a  thing  corre- 
sponding to  each  of  the  terms,  no  harm  is  done  in  speak- 
ing of  the  faculties  of  memory,  imagination,  judgment, 
and  so  forth. 

It  is  obvious  that  there  is  the  same  tendency  to  hy- 
postatise  the  ideas  as  there  is  to  hypostatise  the  facul- 
ties. Indeed  the  two  —  the  ideas  and  the  faculties  — 
have  so  much  in  common  that  they  must  be  distin- 
guished, not  so  much  by  their  fundamental  nature  as 
by  their  reference.  While  both  are,  as  we  have  seen, 
essentially  modes  of  being  conscious,  a  difference  be- 
tween them  may  be  said  to  be  that  while  all  men  have 
the  same  faculties, — though  perhaps  not  of  the  same 
quality, — all  men  are  far  from  having  the  same  ideas. 
The  fact  is  that  ideas  are  forces  that  have  brought  the 
mind  into  touch  with  something  outside  itself.  They 
therefore  either  directly,  or  at  one  or  more  removes, 
have  a  real  connection  with  the  outer  world.  They 
are,  in  consequence,  to  some  extent  dependent  upon  the 
nature  of  the  environment  in  which  the  mind  functions. 
The  same  thing,  however,  may  be  said  about  the  facul- 
ties. Memory  differs  greatly  according  to  the  class  of 
facts  upon  which  it  is  exercised.  We  may  all  be  said 
to  have  good  memories  for  something.  So  with  imag- 
ination and  even  reasoning.  We  always  reason  more 
easily  when  dealing  with  matters  with  which  we  are 
familiar.  This  does  not,  of  course,  mean  that  the  reason 
acts  in  one  way  in  dealing  with  stocks  and  shares  and 
in  another  in  elaborating  metaphysical  theories.  Simi- 
larly, there  are  general  laws  according  to  which  the 
consciousness  acts  in  forming  ideas,  — laws  that  are  the 
same  whether  the  idea  has  to  do  with  the  concrete  or 
the  abstract. 


46     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

A  convenient  way  of  expressing  the  facts  of  the  case 
is  to  say  that  some  modes  of  being  conscious  are  more 
general  than  others,  and  are  called  faculties;  others 
less  general  and  more  affected  by  what  they  act  on  are 
called  ideas.  Since  ideas  are  so  much  determined  by 
our  dealings  with  the  external  world,  they  may  be  said 
in  some  sort  to  represent  the  external  world.  This  is 
how  it  comes  about  that  ideas  are  often  spoken  of  as  if 
they  were  the  material  upon  which  the  faculties  act. 
We  do  not  usually  speak  of  the  mind  acting  upon  the 
imagination  or  the  judgment  —  though,  by  the  way, 
we  sometimes  hear  expressions  among  those  who  pro- 
fess to  improve  the  memory  that  seem  to  imply  an 
action  of  the  mind  on  the  memory  —  while  we  do  speak 
of  its  acting  upon  ideas.  It  is  in  this  sense  that  ideas 
may  be  called  the  content  of  the  mind,  since  they  pro- 
vide a  means  by  which  the  activities  of  the  mind  may 
be  exercised.  Memory,  judgment,  reasoning,  and  the 
other  so-called  faculties  cannot  exist  unless  they  have 
something  to  exercise  themselves  upon.  They  cannot 
carry  on  their  functions  in  vacuo.  They  depend  upon 
the  ideas  to  provide  them  with  the  necessary  material 
to  operate  upon.  This  may  be  accepted  as  a  useful 
form  of  stating  the  case,  but  it  is  necessary  to  be  always 
on  our  guard  against  supposing  that  the  ideas  are  in  any 
real  sense  more  material  than  the  mind  itself.  They 
may  be  that  upon  the  production  and  manipulation  of 
which  the  activity  of  the  mind  expends  itself,  but  it  is 
only  in  this  metaphorical  sense  that  they  can  be  re- 
garded as  material. 

While  we  treat  ideas  as  forces,  we  are  still  in  danger 
of  hypostatisation.  They  are  forces,  no  doubt,  but 
not  independent  forces.  We  sometimes  speak  of  them 


MENTAL  CONTENT  47 

in  a  vague  way  as  acting  upon  the  mind.  But  this  is 
always  a  mistake.  They  never  act  upon  the  mind  for 
the  reason  that  they  themselves  are  only  modes  in 
which  the  mind  acts.  It  has  been  suggested  that  an 
explanation  may  be  effected  by  regarding  the  ideas  as 
one  part  of  the  mind  acting  upon  another  part.  To 
this  no  objection  need  be  raised  so  long  as  it  is  clearly 
recognised  that  the  normal  healthy  mind  is  after  all 
one  and  indivisible.  From  its  very  nature  as  an  or- 
ganism the  mind  must  have  action  and  reaction  going 
on  within  itself,  but  it  must  never  be  forgotten  that  it 
always  remains  one  organic  whole.  Ideas  are  really 
more  or  less  stereotyped  modes  of  being  conscious,  re- 
sulting from  the  more  or  less  constant  reaction  to  the 
same  sort  of  conditions.  A  set  of  conditions  that  is 
continually  recurring  in  absolutely  the  same  way 
naturally  causes  a  very  definite  reaction.1  This  gives 
rise  to  what  may  be  called  an  idea  of  great  force,  say, 
the  idea  of  food.  We  can  think  of  this  idea  and  speak 
about  it  without  really  believing  that  there  is  an  idea 
of  food  apart  from  any  mind.  When  we  say  that  the 
idea  of  food  produces  a  certain  effect  on  the  mind,  what 
we  really  mean  is  that  the  mind  as  a  whole  is  experienc- 
ing a  reaction  resulting  from  its  own  activity  in  a  cer- 
tain direction.  When  several  ideas,  say  food,  hunger, 
poverty,  are  said  to  act  upon  each  other,  what  is  meant 
is  that  the  mind  is  correlating  its  various  activities 
in  relation  to  conditions  that  lie  outside  of  itself. 


1  A  skilled  mechanic's  idea  of  a  hammer  is  quite  different  from 
that  of,  say,  a  writer  of  novels.  Foremen  in  works  tell  us  that  they 
know  the  really  skilled  workman  by  the  way  he  lifts  a  hammer.  His 
reaction  is  quite  different  from  that  of  the  casual  user  of  the  imple- 
ment. 


48     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

As  a  matter  of  phrasing,  therefore,  it  may  be  per- 
missible occasionally  to  speak  of  ideas  as  forces  acting 
and  reacting  upon  each  other.  But  it  has  always  to 
be  kept  in  view  that  this  is  only  a  mode  of  expression, 
a  convenient  figure  of  speech;  and  that  the  mind  is  the 
sole  source  of  the  activity  of  the  ideas. 

From  what  has  been  said  it  follows  that  ideas  are  of 
different  degrees  of  remoteness  from  the  outer  world. 
Certain  ideas  can  be  got  directly  from  without  and  in 
no  other  way.  The  only  way  to  attain  to  an  idea  of 
the  scent  called  Eau  de  Cologne  is  to  experience  the 
sensation  caused  by  smelling  it.  But  the  idea  of  scent 
as  such  is  formed  within.  From  without  we  can  get 
such  ideas  as  red,  blue,  yellow,  and  green ;  but  we  must 
look  within  for  the  idea  of  colour.1  Exposition  is  quite 
unable  to  make  a  congenitally  blind  person  realise  what 
blue  is,  though  it  may  enable  him  to  understand  by 
analogy  from  certain  other  senses  the  sort  of  function 
that  colour  has  in  our  interpretations  of  the  outer  world. 
A  blind  person  may  therefore  be  placed  in  the  position 
of  being  able  to  behave  quite  intelligently  in  relation 
to  certain  questions  involving  colour. 

Since  the  essential  purpose  of  Exposition  is  to  cause 
to  arise  hi  the  mind  of  the  pupil  a  combination  of  ele- 
ments exactly  corresponding  to  a  combination  at  that 
time  existing  in  the  mind  of  the  expositor,  it  is  easy 
to  see  that  in  sensory  matters,  such  as  colour,  taste,  and 
smell,  it  may  well  happen  that  Exposition  fails  because 
the  necessary  elements  are  not  present  in  both  minds. 

1  For  a  very  graphic  and  intelligible  account  of  the  relation  between 
ideas  that  depend  on  outward  stimulus  and  those  that  arise  within, 
see  Huxley's  Hume,  p.  68  ff.  The  whole  of  the  Chapter  on  The  Con- 
tents of  the  Mind  is  very  illuminating. 


MENTAL  CONTENT  49 

But  there  is  a  source  of  danger,  even  when  all  the 
elements  are  present  in  both  minds.  It  is  quite  possible 
that  the  elements  may  be  differently  combined  in  the 
teacher-mind  and  the  pupil-mind.  Sometimes  the 
combination  formed  in  the  pupil's  mind  is  quite  reason- 
able, and  teacher  and  pupil  may  talk  for  long  enough 
about  the  matter  without  discovering  that  they  are 
dealing  with  combinations  that  do  not  agree.  It  was 
only  by  a  chance  statement  in  an  examination  paper 
that  a  teacher  discovered  that  one  of  his  best  pupils  had 
been  for  years  under  the  impression  that  John  Knox 
had  been  hanged.  The  cause  of  the  error  was  a  mis- 
interpretation of  the  remark  made  by  the  teacher  in 
class:  "John  Knox  was  then  sent  to  the  galleys." 
Not  having  heard  of  the  galleys,  and  being  familiar 
with  the  word  gallows,  the  pupil  made  the  natural 
enough  assumption  that  Knox  was  hanged.  The  mis- 
take ought  to  have  been  discovered  by  a  comparison 
of  dates,  but  schoolboys  are  very  willing  to  accept 
on  trust  a  hypothesis  that  fits  in  with  all  the  demands 
of  a  given  lesson.  Usually  the  combination  of  ideas  in 
the  pupil's  mind  is,  as  in  this  case,  quite  intelligible 
to  the  teacher  as  soon  as  it  is  exposed. '  But  occasion- 
ally pupils  who  have  had  quite  a  different  early  train- 
ing from  that  of  their  teachers  may  make  combina- 
tions that  are  unintelligible  even  when  laid  bare.  An 
English  Master  could  not  understand  the  word  smoke 
that  occurred  in  a  Scotch  boy's  essay.  He  gathered 
from  the  context  that  it  was  something  to  eat,  but  could 
not  accept  the  boy's  confident  explanation  that  it  was 
a  small  steak.  Careful  enquiry  brought  out  the  fact 
that  in  the  boy's  family  circle  this  was  the  accepted 
meaning,  its  origin  being  a  corruption  of  the  metrical 


50     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

version  of  the  Hundredth  Psalm.  This  had  been 
taught  to  the  children  before  they  could  read,  by  mak- 
ing them  repeat  the  words  after  the  nurse.  Since  they 
could  not  understand  the  real  sense,  they  had,  from  a 
fundamental  necessity  of  human  thought,  to  supply  a 
sense  of  their  own. 

Know  that  the  Lord  is  God  indeed ; 

Without  our  aid  he  did  us  make :  [did  a  smake] 

We  are  his  flock,  he  doth  us  feed, 

And  for  his  sheep  he  doth  us  take.  [doth  a  steak] 

Custom  legitimised  the  new  substantive  smake  in  the 
family  circle,  and  the  boy  did  not  realise  that  it  was 
not  current  in  the  outside  world. 

Speaking  generally,  the  best  way  of  preventing  serious 
misconceptions  of  the  kind  we  have  been  dealing  with 
is  to  encourage  the  interchange  of  ideas  in  class.  This 
it  is  that  to  some  extent  justifies  the  otherwise  unrea- 
sonable desire  the  teacher  has  for  reproduction  of  knowl- 
edge by  the  pupil.  But  the  best  form  of  reproduction 
is  that  which  applies  knowledge  already  acquired 
rather  than  merely  produces  it  for  inspection.  In  the 
give  and  take  of  genuine  class  teaching  there  is  every 
chance  that  misconceptions  of  all  kinds  will  be  exposed, 
not  necessarily  to  the  teacher  but  to  the  pupils  them- 
selves. Many  a  brilliant  howler  is  lost  to  the  school 
because  the  pupil  himself  learns  in  tune  from  the  work 
that  is  going  on  in  the  class  that  the  answer  he  would 
have  given  had  he  been  unfortunate  enough  to  be  called 
upon  is  not  exactly  the  sort  of  thing  that  would  com- 
mend itself.  The  teacher  has  the  further  satisfaction 
of  knowing  that  not  only  does  this  exchange  of  ideas 
serve  the  particular  ends  of  Exposition,  but  is  in  itself 


MENTAL  CONTENT  51 

of  such  importance  that  it  may  fairly  be  treated  as  a 
fundamental  part  of  the  work  of  education.  Mr. 
H.  G.  Wells,  for  example,  lays  it  down  that  the  chief 
function  of  education  is  to  cultivate  just  this  form  of 
interaction:  — 

"The  pressing  business'of  the  school  is  to  widen  the  range  of  inter- 
course. It  is  only  secondarily  —  so  far  as  schooling  goes  —  or  at  any 
rate  subsequently,  that  the  idea  of  shaping,  or,  at  least  trying  to 
shape,  the  expanded  natural  man  into  a  citizen  comes  in."  * 

It  is  clear  that  for  this  improvement  in  intercourse 
there  must  be  not  only  agreement  hi  the  methods  in 
which  minds  work,  but  substantial  agreement  among 
the  results  of  mental  process.  To  put  the  matter 
baldly,  there  must  be  agreement  between  the  mental 
content  of  teacher  and  pupil  if  there  is  to  be  communion 
between  them.  Exposition  has  for  its  aim  the  estab- 
lishment of  this  agreement.  Even  random  intercourse 
between  teacher  and  pupil  will,  if  continued  long 
enough,  lead  to  the  discovery  of  whatever  disagree- 
ments exist  between  the  two  mental  contents.  But 
for  satisfactory  work  it  is  necessary  to  have  some  com- 
mon standard  to  which  both  contents  may  be  referred, 
so  as  to  bring  out  inconsistencies.  This  standard  is 
to  be  found  in  the  outer  world.  Teacher  and  pupil 
alike  may  test  their  idea-combinations  by  comparison 
with  what  goes  on  in  the  world  around  us.  After  all, 
our  mental  content  is  primarily  made  up  out  of  our  re- 
actions upon  the  outer  world,  and  the  value  of  our  com- 
binations of  ideas  may  be  tested  by  seeing  how  far  they 
will  work  in  relation  to  the  state  of  things  outside  of  us. 
The  combinations  in  every  normal  mind  can  stand  this 

1  Mankind  in  the  Making,  p.  214. 


52     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

test  of  seeing  whether  they  "work"  or  not  in  our  or- 
dinary life.  Unless  our  inner  world  and  the  outer  fit 
into  each  other,  there  is  obviously  something  wrong. 
It  is  not  perhaps  too  strong  a  statement  to  make  that 
a  great  deal  of  exposition  has  for  its  object  the  build- 
ing up  in  the  mind  of  the  pupil  of  great  combinations  of 
ideas  that  correspond  with  the  facts  of  the  outer  world. 
It  is  obviously  of  the  first  importance  that  we  should 
carefully  consider  the  nature  of  the  two  worlds,  and 
particularly  their  relation  to  each  other.  The  outer 
world  is  not  only  a  standard  by  which  to  compare  two 
inner  worlds,  —  the  teacher- world  and  the  pupil-world, 
-  but  the  source  of  the  pattern  upon  which  all  inner 
worlds  are  built. 

The  plain  man  has  no  difficulty  in  believing  that  there 
is  a  world  outside  of  him,  and  that  this  world  is  full  of 
objects  upon  which  he  acts  and  which  in  turn  act  upon 
him.  He  has  no  doubt  whatever  that  he  knows  this 
outer  world,  and  that  it  exists  independently  of  him: 
that  it  has  existed  before  he  was  born,  and  will  exist 
when  he  has  passed  away.  Some  people,  by  reason  of 
greater  opportunities,  may  know  more  of  this  world 
than  do  others,  but  it  does  not  occur  to  the  plain  man 
to  doubt  that  it  is  possible  to  know  it  at  all.  This  is 
left  for  certain  philosophers  who  point  out  that  all  we 
can  ever  know  is  made  up  of  our  own  sensations  and 
the  interactions  and  combinations  of  these  sensations. 
Out  of  the  elements  of  sensation  each  of  us  builds  up  a 
world  of  his  own,  but  thinks  that  world  exists  outside. 
At  first  sight  it  appears  easy  to  demonstrate  the  absurd- 
ity of  a  theory  that  maintains  that  there  is  no  outer 
world  at  all,  but  that  each  of  us  makes  up  a  world  of 
his  own.  So  soon  as  we  try,  however,  we  find  that  the 


MENTAL  CONTENT  53 

theory  has  a  great  deal  of  fight  in  it,  and  that  the 
troublesome  philosophers  have  much  to  say  for  them- 
selves. It  is  found  that  all  our  proofs  ultimately  come 
back  to  the  evidence  of  our  senses.  We  are  confined 
within  the  circle  of  our  own  experience,  and  though  we 
believe  that  there  is  an  outer  world  we  cannot  prove  its 
existence. 

Do  I  see  a  water  carafe  before  me,  or  do  I  only  ex- 
perience certain  sensations  of  light  and  shade?  It 
makes  matters  no  better  when  I  stretch  out  my  hand 
and  feel  the  carafe.  I  only  add  a  bundle  of  new  sen- 
sations. Even  when  I  pour  out  some  water  and  drink 
it,  I  am  no  further  forward.  I  have  only  multiplied 
sensations.  I  have  not  got  beyond  the  range  of  my 
own  personal  experience.  I  believe  that  there  is  a 
carafe  there,  but  I  cannot  get  at  it.  There  is  the  word 
carafe,  and  there  is  the  complex  bundle  of  .sensations 
that  make  up  my  version  of  a  carafe.  But  is  there  a  real 
carafe,  independent  of  me,  —  a  carafe  that  exists  when 
I  am  not  there  to  perceive  it,  a  caraf e-in-itself  ?  This 
problem  of  the  existence  of  a  Thing-in-itself  apart  from 
any  perceiving  being  is  of  great  importance  in  philos- 
ophy, but  for  the  plain  man  it  is  an  excellent  problem 
to  give  up.  Let  us  honestly  beg  the  question.  Let 
us  acknowledge  that  we  cannot  prove  the  existence  of 
an  outer  world  independent  of  us,  and  let  us  at  the 
same  time  take  it  for  granted  that  there  is  an  outer 
world. 

The  very  use  of  the  words  "an  outer  world"  implies 
the  existence  of  a  world  that  is  not  outer.  With  this 
inner  world  we  are  on  friendlier  terms.  We  feel  at  home 
in  it.  We  seem  to  be  free  from  criticism  there.  No 
one  from  without  can  penetrate  within  it.  We  are 


54     EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

ourselves  the  only  persons  capable  of  passing  judg- 
ment on  its  existence  and  nature.  When  we  speak 
of  the  mind's  eye  we  imply  that  there  is  an  inner  world 
that  we  can  look  upon  after  the  fashion  in  which  we 
examine  the  outer  world.  This  would  suggest  a  re- 
semblance between  the  two  worlds.  Most  people  when 
questioned  would  say  that  their  inner  world  is  a  repro- 
duction of  the  outer,  a  sort  of  vaguer  and  less  vigorous 
duplicate  of  what  exists  outside.  As  a  matter  of  fact 
the  inner  world  is  in  part l  a  reproduction  of  our  experi- 
ence of  the  outer  world.  When  we  close  our  eyes  and 
recall  a  past  experience  involving  elements  depending 
on  the  outer  world,  there  is  without  doubt  a  reproduc- 
tion of  what  occurred  in  the  past  including  those  ele- 
ments; our  present  vague  experience  is  similar  to, 
though  feebler  than,  our  past. 

But  this  is  not  quite  the  same  thing  as  to  say  that  the 
inner  world  resembles  the  outer.  Our  mental  picture 
of  a  water  carafe,  even  when  we  are. looking  at  it,  may 
not  at  all  resemble  the  real  carafe,  the  carafe-in-itself. 
All  that  we  can  say  —  but  this  is  quite  enough  for  the 
practical  purposes  of  life  —  is  that  there  is  a  corre- 
spondence between  the  inner  and  the  outer  worlds: 
they  fit  into  one  another,  and  both  remain  constant. 
Whatever  the  carafe-in-itself  is  really  like,  it  always 
causes  the  same  mental  picture  to  arise  when  we  look 
at  it;  it  always  reacts  in  the  same  way  to  the  different 
senses.  So  that  after  all  what  it  is  really  like  is  not  of 
any  moment,  since  we  can  never  by  any  chance  get  at 
this  real  appearance. 

1  Part  of  our  inner  world  is  originated,  if  the  expression  may  be 
permitted,  "on  the  premises."  Our  feelings  and  desires,  for  example, 
must  be  considered  as  essentially  of  the  inner  world  alone. 


MENTAL  CONTENT  55 

We  are  apt  to  picture  the  inner  world  as  made  up  of 
ghostly  water  carafes,  tables,  houses,  mountains,  seas, 
skies,  clouds,  all  combined  in  an  orderly  way,  —  a  sort  of 
well-arranged  storehouse  of  shadowy  things  that  cor- 
respond to  the  things-in-themselves  that  form  the  real 
world.  This  view  may  be  compared  with  that  stage  of 
thought  that  has  been  already  referred  to  as  the  Thing 
stage.  In  this,  the  earliest  stage  of  thought,  the  world 
is  assumed  to  be  made  up  of  a  great  series  of  indepen- 
dent things,  each  existing  by  and  for  itself.  The  stage 
is  illustrated  in  the  drawings  of  children  and  savages. 
There  each  thing  is  drawn  separately,  and  set  down 
on  the  paper  apart  from  the  others.  It  is  only  when 
we  begin  to  see  the  relations  between  the  individual 
things  that  we  realise  that  they  are  not  so  independent 
of  each  other  as  they  seem.  This  marks  the  rise  of  the 
Law  stage,  at  which  relations  are  studied  and  reduced 
to  order  and  classified.  Most  people  pass  through 
both  the  Thing  stage  and  the  Law  stage.  But  com- 
paratively few  reach  the  third  stage  known  as  System, 
in  which  the  Laws  themselves  have  their  meaning 
brought  out  by  being  referred  to  great  general  prin- 
ciples that  dominate  them. 

The  "  things  "  that  make  up  the  inner  world  are  some- 
times referred  to  as  ideas,  concepts,  or  images.  The 
last  name  is  applicable  only  when  we  are  dealing  with 
the  direct  reproduction  of  a  particular  experience.  If 
I  call  up  a  mental  picture  of  a  particular  table  that  I 
am  familiar  with,  I  have  an  image.  But  if  I  merely 
think  about  table  in  general,  I  can  have  no  particular 
picture,  for  I  do  not  know  enough  about  it ;  or  if  you  like, 
I  know  too  much.  I  do  not  know  whether  to  picture 
the  table  as  round  or  square,  or  with  four  legs  or  three 


56     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

or  six,  and  yet  I  know  that  it  may  be  pictured  in  any  of 
these  ways.  This  kind  of  general  idea  that  cannot  be 
reduced  to  a  picture  is  the  kind  that  is  properly  called 
a  concept.  It  must  be  general  enough  to  include  all 
kinds  of  things  that  belong  to  its  class.  The  concept 
table,  for  instance,  must  be  ready  to  include  all  kinds  of 
tables,  —  round,  square,  oblong,  oval,  hexagonal,  — 
but  it  must  never  be  any  of  these.  It  has  to  pay  for 
its  extreme  generality  by  the  loss  of  the  power  ever  to 
become  particular.  The  concept  has  the  power  of 
crystallising  out  into  any  particular  example  of  that 
concept,  but  it  possesses  this  power  only  on  the  condi- 
tion that  it  shall  never  exercise  it,  without  the  result 
ceasing  to  be  a  concept  and  becoming  a  generalised 
image  or  type. 

This  generalised  image  or  type  stands  between  the 
mere  image  and  the  concept.  If  I  look  at  a  particular 
dog  Ponto  here  and  now  present,  I  have  a  percept. 
If  in  the  absence  of  the  dog  I  call  up  in  my  mind  a  pic- 
ture of  this  very  dog  Ponto,  I  have  an  image.  If  now 
I  call  up  in  my  mind  a  picture  of  a  dog  that  is  not  a  re- 
production of  any  particular  dog  that  I  have  ever  seen, 
but  stands  for  a  type  of  all  dogs,  a  sort  of  pattern  of 
dog  in  general,  I  have  a  generalised  image  of  dog. 
This  generalised  image  differs  from  the  concept,  since 
the  latter  cannot  be  represented  as  being  any  special 
kind  of  dog  at  all,  but  can  only  be  thought  about. 
The  generalised  image  of  a  dog  may  be  any  species  of 
dog,  but  it  can  be  of  only  one  species;  it  may  have  any 
colour  I  please  (consistent  with  the  possibilities  of  dog 
nature),  but  it  must  have  some  colour;  and  so  on.  The 
conceptual  dog  has  all  the  qualities  that  are  essential 
to  all  dogs :  it  must  have  four  legs,  a  tail,  two  eyes,  hair, 


MENTAL  CONTENT  57 

and  so  forth ;  it  must  have  colour,  but  no  special  colour; 
must  have  size  and  weight,  but  no  fixed  size  and  weight. 
Thus  the  concept  gains  in  generality  what  it  loses  in 
definiteness. 

Even  in  reading  about  the  concept  one  gets  irritated 
at  its  extreme  elusiveness,  and  in  actual  experience 
people  fall  back  in  despair  upon  the  generalised  image 
and  do  their  thinking  by  means  of  that.  We  shall 
see  later  that  some  writers  object  very  much  to  this 
more  or  less  pictorial  thinking,  and  certainly  it  has  some 
disadvantages.  We  must  not  give  up  the  freedom 
of  thought  that  comes  from  the  extreme  generality 
of  the  concept,  but  on  the  other  hand  we  need  the  sup- 
port of  the  generalised  image  to  assist  the  mind  hi 
dealing  with  concepts.  When  we  use  the  generalised 
image,  we  are  really  thinking  of  "dog  in  general," 
but  by  means  of  a  concrete  particular  dog  —  though 
which  particular  dog  is  irrelevant. 

The  question  may  now  be  asked  whether  the  inner 
world  is  made  up  of  concepts  or  images.  It  would 
appear  that  there  is  room  for  nothing  but  images. 
How  can  one  construct  a  world  in  which  tables  are  not 
allowed  to  be  any  particular  kind  of  tables,  but  only 
tables  in  general,  that  can  be  thought  about  but  not 
represented  ?  This  difficulty  brings  out  the  distinction 
between  the  static  and  the  dynamic  view  of  the  concept. 
Each  of  the  views  is  sound  though  each  emphasises 
a  different  aspect. 

The  static  view  of  the  inner  world  is  that  it  is  made 
up  of  a  great  mass  of  more  or  less  attenuated  represen- 
tations of  "things,"  all  arranged  so  as  to  fit  into  each 
other's  qualities  and  positions.  But  such  a  world  is 
inert,  dead.  It  exists  only  to  be  examined  by  logical 


58     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

persons  who  are  concerned  about  definition  and  classi- 
fication. For  the  ordinary  needs  of  life  there  must  be 
the  possibility  of  interaction  among  the  elements  that 
make  up  the  inner  world.  It  is  here  that  the  dynamic 
view  has  the  advantage.  The  concept  of  a  table  is  no 
longer  to  be  treated  as  a  mere  group  of  the  essential 
qualities  of  a  table,  but  as  a  force  determining  particu- 
lar lines  of  action.  If  you  ask  an  ordinary  intelligent 
person  what  a  table  is,  you  will  probably  find  that  he 
has  some  little  difficulty  hi  saying  precisely.  Does 
this  mean  that  because  he  cannot  define  a  table  he  does 
not  know  what  a  table  is  ?  Assuredly  not.  He  is  able 
to  behave  intelligently  hi  relation  to  tables.  To  under- 
stand a  term  it  is  not  necessary  that  one  should  be  able 
to  define  it. 

Definition  has  no  doubt  its  proper  place.  The 
moment  we  need  to  discriminate  carefully  between 
different  terms,  we  have  to  define  them  more  or  less 
accurately,  and  more  or  less  consciously.  ,  But  we  must 
not  let  the  definition  dominate  us.  If  we  are  asked: 
what  is  chalk  ?  we  may  turn  to  the  dictionary  and  find 
that  it  is  "a  soft  earthy  substance  of  a  white,  grayish, 
or  yellowish  white  colour,"  etc.,  or  we  may  simply  say: 
it  is  something  to  write  on  a  blackboard  with,  or  to  im- 
prove the  head  of  a  billiard  cue  with,  or  to  make  car- 
bonic acid  out  of.  Some  are  inclined  to  say  that  these 
are  purposes  to  which  chalk  can  be  applied,  but  that 
they  do  not  tell  us  what  it  is.  Chalk,  they  say,  is  a 
chemical  compound  represented  by  the  formula  CaCO,, 
that  and  nothing  else.  But  chalk  is  as  much  a  thing  to 
write  with  as  it  is  a  chemical  compound.  This  is  a 
world  in  which  we  react  upon  chalk  in  various  ways, 
one  of  them  being  a  chemical  way;  but  this  way  is  no 


MENTAL  CONTENT  59 

more  fundamental  than  the  others.  We  must  remember 
that  classification  is  of  the  mind  and  not  of  the  world. 
We  find  it  necessary  for  our  human  needs  to  classify 
objects,  but  this  is  for  our  convenience,  and  is  not  at 
all  binding  upon  nature.  Among  young  students  there 
is  sometimes  a  certain  impatience  with  Nature.  They 
get  their  carefully  prepared  classification  in  books,  and 
are  not  a  little  indignant  with  Nature  when  she  does 
not  see  her  way  to  fit  into  the  arrangement  in  every 
case.  For  example,  there  is  a  troublesome  little  Aus- 
tralian mammal,  called  the  ornithorhynchus  anatinus, 
that  is  the  despair  of  the  taxonomist.  It  is  a  web- 
footed  quadruped,  with  a  bill  like  a  duck  ;  and  it  lays 
eggs  like  a  bird  or  reptile.  There  is  no  place  for  this 
creature  in  any  of  the  recognised  classes,  and  to  make 
a  new  class  for  it  by  itself  is  extremely  disconcerting. 
There  is  a  touch  of  remonstrance  even  in  the  state- 
ment of  the  sober  taxonomist :  — 

"The  lowest  order  of  the  Mammalia  is  that  of  the  Monotremata, 
constituting  by  itself  the  division,  Omithodelphia,  and  containing 
only  two  genera,  both  belonging  to  Australia  —  namely,  the  Ornitho- 
rhynchus and  the  Echidna."  * 

This  is  not  the  place  to  show  the  value  of  such  a 
hybrid  specimen  in  leading  us  to  discover  the  real 
nature  of  the  different  classes  to  which  it  might  claim 
doubtful  admission,  and  especially  in  making  clear  the 
relation  between  these  classes.  What  is  more  germane 
to  our  subject  is  the  question  of  what  place  is  to  be 
found  in  the  mental  content  for  such  exceptional  cases. 
Ruled  out  of  the  well-known  bird  and  reptile  classes 
and  thrust  into  a  little  class  of  its  own,  the  ornitho- 
rhynchus is  still  intelligible  to  us ;  we  at  least  know  what 

1  H.  A.  Nicholson :  Manual  of  Zoology,  p.  630. 


60     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

we  mean  in  speaking  of  it.  Everyone  who  has  read  this 
chapter  thus  far  has  formed  some  sort  of  idea  of  the 
creature,  and  there  are  as  many  ideas  of  the  ornitho- 
rhynchus  as  there  are  people  who  use  the  term.  If  the 
reader  examines  his  idea,  he  will  find  that  it  is  modified 
by  what  he  knows  about  Australia,  about  ducks,  about 
bills,  about  mammals,  quadrupeds,  eggs,  birds,  reptiles, 
and  even  Greek. 

In  spite  of  all  such  troublesome  exceptions  there  is  a 
use  for  the  exact  classification  that  admits  of  no  devia- 
tion from  the  strict  marks  that  distinguish  each  group. 
Classification  is  of  the  mind,  and  so  is  the  idea  of  the 
unclassifiable  ornithorhynchus.  But  each  represents 
a  different  department  of  mental  activity.  The  limita- 
tions imposed  by  the  laws  of  classification  are  logical; 
the  additional  materials  supplied  from  individual  ex- 
perience of  exceptions  to  those  laws  have  to  be  dealt 
with  as  psychological  units. 

In  the  next  chapter  ideas  will  be  treated  as  active. 
Here  it  will  be  enough  to  deal  with  them  as  the  elements 
out  of  which  certain  combinations  are  to  be  formed. 
In  Exposition  the  teacher  has  already  in  his  mind  a 
certain  more  or  less  elaborate  combination  of  ideas, 
forming  the  expositandum.  The  pupil  may  have  all 
the  necessary  ideas  lying  about  loose,  as  it  were.  It  is, 
then,  the  teacher's  business  to  build  up  those  ideas 
in  the  pupil's  mind  into  the  desired  whole.  It  may  be 
(hi  fact,  this  is  the  ordinary  case)  that  the  pupil  has  only 
certain  of  the  needful  ideas  at  his  disposal.  In  this 
case  the' teacher  has  to  present  the  necessary  new  ideas 
as  well  as  to  arrange  the  ideas  at  present  possessed  by 
the  pupil. 

Exposition  may  therefore  be  regarded  as  essentially 


MENTAL  CONTENT  61 

a  constructive  process,  and  under  ideal  conditions  it 
need  never  be  destructive.  In  building  up  knowledge, 
fact  should  be  added  to  fact  in  such  a  way  that  it  is 
never  necessary  to  undo  what  has  been  done.  A  com- 
bination of  ideas  once  formed  should  be  for  all  time. 
Something  approaching  this  ideal  state  of  affairs  may 
be  reached  in  the  case  of  subjects  that  are  removed  from 
the  ordinary  interests  of  everyday  life.  In  certain 
branches  of  Mathematics,  and  in  the  higher  reaches  of 
many  of  the  other  school  subjects,  it  is  possible  for  the 
teacher  so  to  dominate  the  presentation  of  entirely 
fresh  matter  that  each  new  fact  falls  exactly  into  its 
appropriate  place.  In  teaching  Latin,  for  example, 
there  is  nothing  to  prevent  the  master  from  deliberately 
determining  beforehand  the  exact  order  in  which  the 
various  points  shall  be  presented  to  the  pupil.  Yet 
even  when,  as  in  this  case,  the  arrangement  of  the  pres- 
entation is  entirely  in  the  hands  of  the  teacher,  it  some- 
times occurs  that  in  order  to  give  complete  understand- 
ing of  a  given  fact  two  other  facts  must  be  presented 
simultaneously.  Neither  without  the  other  will  be 
capable  of  throwing  light  upon  the  point  to  be  explained, 
and  since  in  actual  practice  one  must  precede  the  other, 
it  is  occasionally  necessary  to  present  one  because,  on 
the  whole,  it  is  somewhat  more  relevant  than  the  other, 
and  yet  the  fact  that  has  lost  precedence  may  hi  cer- 
tain respects  deserve  to  come  first. 

Apart  from  this  difficulty  that  is  inherent  in  the  na- 
ture of  things,  there  is  the  ever  present  trouble  that  we 
can  in  almost  no  case  start  quite  fair.  We  have  very 
seldom  indeed  the  clean  sheet  that  ideal  exposition 
demands.  Our  pupils  generally  come  to  us  with  their 
mental  content  already  fixed  with  regard  to  many  of 


62     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

the  matters  we  have  to  deal  with.  Accordingly  we 
cannot  limit  ourselves  to  the  building  up  of  new  wholes 
out  of  entirely  fresh  elements.  Our  elements  are  not 
fresh,  and  there  are  wholes  already  in  existence. 

Thus  it  comes  about  that  there  is  a  destructive  as 
well  as  a  constructive  stage  in  Exposition.  When  the 
existing  combination  of  ideas  is  not  to  our  satisfaction, 
we  must  demolish  it  before  we  can  begin  to  reconstruct 
it  in  the  way  we  desire.  We  are  all  familiar  with  what 
takes  place  when  a  pupil  changes  from  one  teacher  of 
the  violin  to  another.  Almost  invariably  the  master 
is  determined  to  have  his  style  of  execution  adopted, 
and  in  order  to  secure  this  insists  upon  his  pupil  begin- 
ning again  at  the  very  beginning.  When  the  violinist 
turns  back  his  pupil  in  this  way,  his  idea  is  to  break  up 
the  previously  formed  coordination  of  muscular  actions, 
and  establish  in  its  place  a  coordination  that  will  fit 
in  with  the  later  complex  movements  demanded  by 
the  approved  execution.  In  ordinary  exposition  it  is 
seldom  that  we  require  to  carry  destructive  work  so  far. 
It  is  usually  unnecessary  to  reduce  a  given  combination 
to  its  elements  in  order  to  correct  some  false  colloca- 
tion. The  pupil  may  have  the  view  that  the  further 
south  one  goes  the  warmer  it  becomes.  All  his  ex- 
perience warrants  him  in  maintaining  this  view,  and 
he  holds  it  with  some  vigour.  It  is  not  at  all  necessary 
that  the  complex  that  corresponds  to  " south"  in  his 
mind  should  be  reduced  to  its  elements  and  painfully 
reconstructed  on  correct  lines.  All  that  is  necessary 
is  to  break  up  the  existing  unwarrantable  connection 
between  south  and  increasing  temperature.  To  the 
pupil  south  still  remains  south  in  every  other  attribute, 
but  the  new  element  of  relativity  is  introduced,  and  the 


MENTAL  CONTENT  63 

pupil  learns  that  while  moving  to  the  south  always  in- 
volves change  of  average  temperature,  it  does  not  al- 
ways involve  the  same  kind  of  change.  In  ordinary 
exposition  it  is  usually  sufficient  to  stop  far  short  of 
ultimate  analysis,  and  to  begin  the  reconstructive  pro- 
cess with  units  that  are  not  nearly  the  lowest  possible. 

Further,  it  has  to  be  noted  that  the  destructive  pro- 
cess may  be  necessary,  not  because  the  combination  is  in 
itself  objectionable,  but  because  there  is  a  need  for  the 
elements  of  which  it  is  composed,  in  order  to  build  up 
a  new  complex.  In  a  given  combination  certain  ele- 
ments become  so  firmly  welded  together  that  their 
individual  existence  is  overlooked,  and  it  becomes  the 
teacher's  business  to  break  up  the  fixed  combination 
so  that  the  elements  may  become  available  in  other 
connections. 

In  the  ultimate  resort,  however,  Exposition  as  Ex- 
position is  a  process  of  building  up.  The  destructive 
process  is  no  doubt  important,  and  indeed  essential, 
but  it  is  none  the  less  merely  preparatory  to  the  real 
work  of  Exposition  which  is  constructive.  Learning 
a  subject  means  really  the  building  up  of  various  ideas 
into  an  organised  whole  in  which  each  finds  its  appro- 
priate place.  Ideas  in  this  sense  must  be  regarded  as 
representing  activities.  It  is  only  when  fact  has  be- 
come faculty  that  we  have  really  learned. 

It  is  clear  that  when  we  speak  of  a  combination  of 
mental  elements,  we  give  no  indication  of  the  extent  to 
which  the  combination  is  carried.  In  Exposition  we 
have  frequently  to  seek  out  simpler  ideas  in  order  to 
explain  those  that  are  more  complex.  The  unit  of 
Exposition  therefore  becomes  important.  Naturally 
the  ultimate  unit  is  the  individual  idea.  But  in 


64     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

practice  the  simple  individual  idea  is  found  to  be  very 
difficult  to  separate  out  and  manipulate.  It  has  always 
a  strong  tendency  to  take  to  itself  other  elements  and 
appear  as  a  complex.  In  what  are  called  "Object 
Lessons"  hi  school  there  is  a  strong  tendency  on  the 
part  of  the  teacher  to  wander  into  an  explanation  of  the 
qualities  of  objects,  and  to  lose  sight  of  the  object  itself. 
The  teacher  yields  to  the  lust  of  analysis.  Whatever 
the  subject,  the  lesson  is  apt  to  drift  into  a  discussion 
of  the  meaning  of  such  terms  as  opaque,  brittle,  elastic, 
fluid,  friable,  metallic.  But  while  the  teacher's  ten- 
dency is  thus  towards  abstraction,  the  pupils  are  in- 
clined the  other  way,  and  are  found  to  be  continually 
interpreting  the  abstract  terms  in  connection  with  con- 
crete objects.  When  the  teacher  wishes  to  elicit  the 
idea  of  whiteness,  he  gets  from  the  pupil  the  answer 
chalk.  "What  do  you  mean  by  brittle?"  asks  the 
teacher,  and  the  natural  answer  is  glass. 

The  unit  of  exposition  must  naturally  vary  with  the 
stage  of  advancement  of  the  pupil.  As  we  progress  in  a 
subject  the  unit  naturally  grows  bigger.  Very  many 
errors  hi  exposition  arise  from  using  a  bigger  unit  than 
the  state  of  advancement  of  the  pupils  warrants. 


CHAPTER  III 
MENTAL  ACTIVITY 

THE  Laws  of  Thought  as  Thought  are  purely  general 
and  abstract.  They  take  no  account  of  the  material 
upon  which  the  mind  acts.  Yet  this  material  is  of  the 
very  essence  of  Exposition.  We  have  seen  that  under 
certain  reservations  we  may  regard  ideas  as  the  material 
upon  which  the  mind  operates.  This  is  their  passive 
aspect.  Ideas  in  this  relation  are  regarded  as  the  mere 
furniture  of  the  mind,  its  stock  in  trade,  its  acquired 
possessions.  So  treated  they  are  termed  "presented 
content." 

Ideas  are  also  said  to  possess  a  certain  degree  of 
"  Presentative  activity,"  which  may  be  generally  de- 
fined as  the  power  to  force  an  admission  into  conscious- 
ness. Every  idea  that  has  ever  been  in  consciousness 
has  by  that  very  fact  acquired  a  certain  degree  of  this 
activity,  and  this  amount  is  increased  every  time  the 
idea  finds  its  way  back  into  consciousness.  It  is  con- 
ceivable that  at  a  given  moment  the  presentative  ac- 
tivity of  every  idea  that  has  ever  passed  through  a  given 
mind  should  be  tested  and  registered.  If  this  practically 
impossible  feat  could  be  accomplished,  we  would  have  a 
systematic  arrangement  of  ideas  in  order  of  their  accu- 
mulated presentative  activity  for  that  mind.  Now  it 
is  clear  that  if  this  state  of  affairs  represented  the  whole 
truth,  only  a  few  ideas  would  ever  get  into  the  mind  at 
p  65 


66     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

all,  unless  it  were  able  to  take  in  an  unlimited  number 
of  ideas  at  a  time.  For  naturally  those  with  the  great- 
est presentative  activity  would  force  their  way  into  the 
mind  and  would  resist  all  the  attempts  of  the  less  power- 
ful ideas  to  dislodge  them.  As  a  matter  of  fact,  how- 
ever, ideas  with  comparatively  little  accumulated  pre- 
sentative activity  may  acquire  a  temporary  power 
sufficient  to  dislodge  for  the  moment  all  others.  Sup- 
pose we  are  studying  Shakespeare.  The  ideas  called 
up  by  his  plays  have  in  the  course  of  time  acquired  a 
great  accumulation  of  presentative  activity.  Yet  at 
the  moment  of  our  most  intense  study  of  As  You  Like 
It  a  sudden  street  call  may  displace  Rosalind  and 
Orlando  from  our  thoughts  in  favour  of  shrimps  or  cat's 
meat.  To  be  sure  the  Shakespearian  ideas  immediately 
resume  their  place  in  virtue  of  their  greater  accumu- 
lated activity  as  individual  ideas,  and  also  because  of 
the  support  they  give  to  one  another  as  parts  of  an 
organised  group. 

For  ideas  do  not  remain  hi  the  consciousness  as  iso- 
lated units.  They  are  always  bound  more  or  less 
closely  to  the  other  ideas  that  happen  to  be  present  in 
the  consciousness  with  them.  It  is,  of  course,  impossible 
to  say  how  many  ideas  may  be  in  the  consciousness  at 
any  one  time.  The  number  must  vary  greatly  accord- 
ing to  the  degree  of  concentration  that  marks  the 
moment.  It  may  be  said  that  if  there  are  one  or  two 
particularly  active  ideas  in  the  mind,  there  is  no  room 
for  any  others.  The  same  fact  may  be  more  truly  ex- 
pressed by  saying  that  the  consciousness  is  sometimes 
concentrated  on  a  few  points  and  sometimes  spread  over 
a  large  number.  Except  in  pathological  cases  there 
are  always  more  than  one  idea  present  in  the  conscious- 


MENTAL  ACTIVITY  67 

ness,  and  in  normal  cases  there  is  usually  a  more  or  less 
uniform  distribution  of  the  available  consciousness 
among  the  ideas  presented.  It  is  common  to  speak  of 
the  " field  of  consciousness"  as  representing  the  area 
within  which  ideas  are  active.  This  field  is  often  re- 
garded as  being  round,  perhaps  from  a  more  or  less  con- 
scious comparison  with  the  field  of  vision  as  dealt  with 
in  linear  perspective,  where  it  is  represented  by  the  base 
of  the  cone  of  visual  rays. '  Within  this  field  some  of  the 
ideas  appeal  to  us  at  a  given  moment  much  more  than 
do  others.  We  figure  those  ideas  to  ourselves  as  oc- 
cupying the  centre  of  the  field,  and  therefore  we  call 
them  focal.  Those  somewhat  removed  from  the  centre 
may  be  called  subfocal,  those  near  the  circumference 
submarginal,  and  those  on  the  circumference  marginal. 
The  nearer  an  idea  is  to  the  centre,  the  greater  its  share 
of  consciousness.  It  is  obvious  that  the  same  fact  may 
be  expressed  by  saying  that  the  ideas  with  the  strongest 
presentative  activity  occupy  the  centre,  and  those  of 
less  activity  have  to  content  themselves  with  a  place  in 
the  subfocal,  submarginal,  or  marginal  area.  In  other 
words  we  may  speak  literally  of  the  distribution  of  con- 
sciousness, or  metaphorically  of  the  activity  of  the  ideas. 
In  order  to  make  this  figure  workable  it  is  probably 
necessary  to  assume  that  the  field  of  consciousness  is 
capable  of  more  or  less  rapid  change  of  area.  Some- 
times it  is  very  small  and  contains  only  a  few  ideas. 
Under  such  circumstances  the  distinction  between  focal 
and  marginal  almost  disappears;  the  few  ideas  present 
are  practically  all  focal.  At  other  times  the  area  is 
wide,  and  the  number  of  ideas  correspondingly  in- 
creased. Here  the  focal  ideas  are  not  so  intense,  as 
in  the  case  of  the  smaller  field,  but  they  are  much  more 


68     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

intense  than  are  those  in  the  outlying  regions.  We  have 
to  assume  that  the  total  amount  of  consciousness  avail- 
able at  a  given  moment  is  limited,  and  that  therefore 
the  problem  is  largely  one  of  distribution. 

There  is  danger  of  overrigidity  in  the  figure.  No 
exact  line  of  demarcation  can  be  drawn  between  focal 
and  subfocal  near  the  centre,  and  none  between  mar- 
ginal and  submarginal  near  the  circumference.  The 
figure  of  the  field  has  the  advantage  that  it  renders 
impossible  the  older  view  that  really  implied  that  only 
one  idea  at  a  time  passed  through  the  consciousness. 
In  psychology  it  is  frequently  necessary  to  correct  one 
metaphor  by  means  of  another.  The  "field  of  con- 
sciousness" figure  corrects  the  old  linear  view  that  con- 
fined itself  to  the  seriatim  procession  of  the  focal  ideas, 
but  in  its  turn  errs  by  confining  itself  to  one  plane. 
Professor  James's  1  figure  of  the  "stream  of  conscious- 
ness" or  the  "stream  of  thought"  with  his  various 
graphic  illustrations  emphasises  the  element  of  bulk  or 
mass  hi  our  mental  content.  It  has  the  further  advan- 
tage of  indicating  a  procession  of  force  as  well  as  mate- 
rial. In  the  field  figure  there  is  merely  the  suggestion  of 
a  place  where  the  ideas  may  disport  themselves.  The 
stream  figure,  by  its  very  nature,  implies  the  crowding 
hi  of  new  matter  and  the  passing  away  of  old.  Nat- 
urally the  figure  must  not  be  too  closely  pressed,  for 
in  thought  there  is  usually  a  core  of  preferred  ideas  that 
retain  their  place  in  the  middle  of  the  stream,  while 
a  great  body  of  ideas  pass  rapidly  along  at  the  margins; 
whereas  in  a  real  river  the  opposite  is  the  case,  for  the 
water  in  the  middle  moves  more  rapidly  than  the  water 
at  the  margins. 

1  Principles  of  Psychology,  Vol.  I,  p.  279  ff. 


MENTAL  ACTIVITY  69 

It  will  probably  be  well  now  to  pass  on  to  a  more 
general  statement  of  the  case  in  less  figurative  terms. 
The  word  continuum  is  becoming  more  and  more  pop- 
ular as  a  term  to  describe  the  mental  content  at  any 
given  moment.  The  word  indicates  a  great  mass  of 
ideas  held  before  the  mind;  but  the  ideas  are  not  re- 
garded as  lying  loose,  they  are  bound  to  one  another, 
they  form  a  more  or  less  homogeneous  whole.  The 
binding  force  may  be  said  to  be  a  common  purpose  or 
a  common  interest.  The  purposive  interest  that  dom- 
inates the  continuum  may  be  concentrated,  and  may 
tend  therefore  to  limit  the  number  of  elements;  or 
it  may  be  diffused,  and  may  take  in  a  large  number  of 
elements.  But  whether  the  elements  of  a  continuum 
are  few  or  many,  they  never  remain  long  fixed  in  the 
same  relation  to  one  another.  Constant  change  is  of 
the  essence  of  the  continuum.  There  is  a  continuous 
coming  and  going  of  mental  elements.  When  we  are 
thinking  steadily  on  a  given  subject,  the  core  of  the 
continuum  will  be  fairly  large  in  proportion  to  the 
whole,  and  will  remain  fairly  constant;  whereas  in  easy 
general  talk,  or  in  attending  to  the  details  of  ordinary 
life,  the  continuum  is  liable  to  violent  changes  in  its 
elements,  and  the  core  is  restricted  to  that  minimum 
of  common  elements  that  ensures  the  preservation  of 
our  sense  of  identity. 

We  have  treated  the  elements  that  form  a  continuum 
as  if  they  were  separate  from  each  other.  No  doubt 
in  ultimate  analysis  the  contents  of  any  continuum 
could  thus  be  reduced  to  independent  elemental  units; 
but  in  practice  it  is  found  that  ideas  have  a  tendency 
to  group  themselves.  Under  identical  circumstances 
in  the  experience  of  the  same  individual  certain  con- 


70     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

tinuums  are  likely  to  have  almost  identical  content. 
But  even  in  a  continuum  that  has  never  before  invaded 
consciousness  it  will  be  found  that  its  elements  are  more 
or  less  definitely  arranged  in  groups.  These  groups  of 
ideas,  sometimes  known  as  apperception  masses,  have 
been  formed  by  the  co-presentation  in  consciousness 
of  the  ideas  hi  question.  They  must  therefore  have 
formed  part  of  previous  continuums,  though  their  ac- 
companiments in  any  two  of  these  continuums  may 
never  have  been  the  same.  In  considering  how  these 
groups  have  been  formed  it  will  be  well  in  the  first  place 
to  begin  from  the  side  of  the  mind  rather  than  from 
that  of  the  idea,  hi  order  to  counteract  the  tendency  to 
regard  the  ideas  as  things  independent  of  the  mind. 
After  the  mental  activity  has  been  acknowledged  there 
will  be  less  harm  in  working  out  the  attractive  mechan- 
ism of  apperception  hi  terms  of  ideas. 

In  the  older  fashioned  theories  of  the  Association  of 
Ideas  certain  general  principles  were  laid  down  that 
were  useful  enough  so  far  as  they  went.  But  even 
when  they  were  gathered  up  into  one  generalisation,  as 
hi  Sir  William  Hamilton's  Redintegration,1  they  gave 
little  help  hi  the  way  of  explaining  the  building  up  of 
great  groups  of  ideas,  though  they  certainly  explained 
very  ingeniously  many  mental  phenomena  after  they 
had  occurred.  Fr.  Paulhan,  in  his  UActivite  Mentale, 
works  out  a  more  active  system  of  association  which 
ultimately  resolves  itself  into  two  great  laws  —  a  posi- 
tive and  a  negative.  The  positive  law  he  calls  the  law 
of  systematic  association.  It  runs :  — 

"  Every  psychical  fact  tends  to  associate  to  itself,  and  cause  to 
develop,  the  psychical  facts  which  may  harmonise  with  it,  which 

1  Lectures  on  Metaphysics,  Lecture  XXXII,  p.  238. 


MENTAL  ACTIVITY  71 

may  strive  with  it  towards  a  common  goal  or  for  complementary 
ends,  which,  along  with  it,  may  be  able  to  form  a  system." 1 

The  negative  law  deals  with  inhibition  or  arrest :  — 

"Every  psychical  phenomenon  tends  to  prevent  the  production 
or  development,  or  to  cause  the  disappearance,  of  psychical  phe- 
nomena which  cannot  be  united  to  itself  according  to  the  law  of  sys- 
tematic association ;  that  is  to  say,  which  cannot  be  united  with  it 
for  a  common  end." z 

These  two  laws,  working  under  the  impulse  of  purpose, 
secure  that  the  various  modes  of  being  conscious  that 
are  of  special  value  to  the  mind  shall  recur  with  suffi- 
cient frequency  to  establish  an  ease  in  reinstating  them- 
selves whenever  they  are  called  for,  and  we  have  thus 
the  beginning  of  the  activity  that  results  in  the  organi- 
sation of  the  mental  processes  in  relation  to  the  mental 
content.  What  we  call  organised  groups  of  ideas  or 
apperception  masses  may,  from  another  point  of  view, 
be  regarded  as  organised  modes  of  being  conscious. 

Treating  the  matter  now  from  the  point  of  view  of 
the  ideas,  it  is  to  be  noticed  that  the  two  most  important 
laws  correspond  hi  general  with  those  of  Paulhan. 
Ideas  that  are  called  contrary  ideas,  that  is,  ideas  that 
belong  to  the  same  category  but  differ  within  that  cate- 
gory (such  as  blue,  green,  and  yellow,  which  come  under 
the  same  category  of  colour,  but  differ  inasmuch  as  they 
are  different  colours),  arrest  one  another.  This  means 
that  in  the  competition  to  enter  consciousness  contrary 
ideas  oppose  each  other,  do  everything  they  can  to  eject 
each  other,  and  finally  as  the  result  of  the  strife  one  or 
other  succeeds  in  effecting  an  entrance  and  in  expelling 
the  other.  It  may  be  objected  that  two  contrary  ideas 
may  occupy  the  consciousness  at  the  same  time.  We 

1  L'Activite  Mentale,  p.  88.  2  Ibid.,  p.  221. 


72     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

amy  think  of  a  geranium  with  green  leaves  and  red 
petals.  But  here  the  ideas  of  red  and  green  are  not 
treated  by  the  mind  as  mere  colours,  but  only  as  aspects 
of  a  whole.  We  think  of  a  geranium  in  fact,  not  of  red 
and  green.  This  brings  out  the  distinction  between 
the  having  of  an  idea  and  the  realising  of  that  idea. 
When  we  merely  have  an  idea,  or  admit  an  idea  to  the 
mind,  we  treat  it  as  a  more  or  less  representative  ele- 
ment that  embodies  a  meaning  or  is  significant  of 
something  else.  To  realise  the  idea  of  red  we  must 
concentrate  upon  it  all  the  forces  that  are  appropriate 
to  an  idea  of  colour,  and  in  so  doing  we  are  drawing  off 
all  the  force  that  might  otherwise  have  been  concen- 
trated upon  green  or  some  other  colour.  In  so  far  then 
as  red  and  green  as  colours  both  retain  their  place  in 
consciousness,  neither  is  fully  realised,  and  their 
relation  to  each  other,  and  to  the  mind  in  which  they 
are  found,  is  one  of  unstable  equilibrium,  the  force 
of  each  being  spent  in  trying  to  further  its  own  fuller 
development,  and  to  eject  the  other  from  conscious- 
ness. 

The  law  of  systematic  association,  on  the  other  hand, 
applies  to  those  ideas  that  are  known  as  disparate. 
These  ideas  have  no  inherent  relation  to  each  other; 
they  do  not  belong  to  the  same  category,  and  so  can  be 
formed  into  any  sort  of  complexes  that  circumstances 
may  favour.  There  is  no  inherent  connection,  so  far  as 
we  know,  between  a  grey  overcoat,  a  white  horse,  and 
Napoleon  I,1  yet  by  the  actual  collocation  of  these  ideas 
in  history  they  form  a  complex  that  has  a  certain  sta- 
bility of  its  own.  Taking  that  overworked  example 

1  If  we  could  view  these  elements  sub  specie  ceterniiatis,  no  doubt 
we  could  discover  a  sufficient  cause  for  their  collocation. 


MENTAL  ACTIVITY  73 

of  the  psychologists,  the  orange,  we  find  that  its  quali- 
ties are  grouped  together  in  the  same  way.  All  the 
ordinary  complexes  of  life  are  built  up  in  accordance 
with  the  law  of  systematic  association,  or  the  law 
of  complication,  as  it  may  be  called,  when  regarded 
from  the  point  of  view  of  .the  ideas  rather  than  of  the 
mind. 

Besides  the  two  forces  of  complication  and  arrest 
there  is  a  third  that  has  to  be  taken  into  account  in 
connection  with  the  interaction  of  ideas.  This  is 
known  as  fusion.  When  an  idea  recurs  in  the  mind 
it  fuses  with  the  traces  it  left  at  its  previous  visit. 
It  is  by  this  force  of  fusion  that  our  elementary  ideas 
acquire  the  stability  that  is  so  necessary  as  a  founda- 
tion for  the  whole  superstructure  of  ideas.  In  the 
case  of  two  complexes  being  brought  into  conscious- 
ness together,  all  the  similar  elements  in  the  two  fuse, 
all  the  disparate  elements  proceed  to  form  a  new  and 
more  elaborate  complex,  while  the  contrary  ideas 
arrest  each  other.  It  must  not  be  supposed  that 
fusion  is  limited  to  the  substantive  elements  of  thought. 
Similar  relations  that  recur  fuse  as  to  their  common 
elements,  and  strengthen  the  idea  of  their  particular 
class  of  relation.  The  compelling  power  of  analogy 
owes  much  to  fusion. 

Fusion  is  always  at  work  in  the  mind.  For  the  com- 
mon elements  in  the  different  groups  strengthen  each 
other  as  elements,  every  time  they  appear  in  conscious- 
ness. Two  ideas  that  are  contrary  to  each  other,  and 
therefore  seek  to  arrest  each  other,  still  so  react  upon 
the  rest  of  the  mental  content  that  by  fusing  with  sim- 
ilar elements  in  that  content  they  really  acquire  each 
a  little  more  strength;  that  is,  increase  their  accumu- 


74     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

lated  preservative  activity,  even  while  being  driven  out 
of  consciousness  for  the  moment  by  a  stronger  rival. 

Complication  is  obviously  the  converse  of  analysis. 
After  we  have  broken  up  one  group  of  ideas  in  order  to 
reconstruct  the  elements  into  another,  the  rebuilding 
is  largely  a  matter  of  complication.  Naturally  fusion 
is  going  on  parallel  with  complication;  for  all  the  ele- 
ments common  to  the  two  groups,  instead  of  forming  a 
complex,  merely  go  to  strengthen  each  other.  But 
arrest  is  also  present  hi  complication.  Its  main  work 
in  forming  new  groups  is  to  prevent  the  accumulation 
of  unnecessary  details. 

Every  idea  seeks  to  introduce  into  consciousness  all 
the  other  ideas  with  which  it  has  formed  connections. 
An  idea  therefore  that  forms  a  part  of  many  apper- 
ception masses  has  a  dangerous  tendency  to  recall  too 
many  ideas  with  which  it  is  allied  in  different  groups. 
Of  the  ideas  thus  invited  into  the  consciousness  some 
set  up  a  process  of  fusion,  and  others  of  complication, 
but  a  large  number  are  cut  off  by  the  process  of  arrest. 
If  it  were  not  so,  thinking  would  become  impossible. 
The  mind  would  be  smothered  under  the  crowd  of 
ideas. 

Exposition  consists  fundamentally  of  the  establish- 
ment of  new  combinations  of  ideas,  or  of  the  making 
clear  and  strong  combinations  that  at  present  exist  in  a 
vague  and  feeble  way.  To  give  the  new  combinations 
strength  we  must  have  as  great  an  amount  of  fusion  as 
is  possible  under  the  circumstances.  Richness  and 
breadth  depend  upon  complication.  Clearness  and 
definiteness  are  gained  by  arrest.  That  all  three  pro- 
cesses may  produce  their  best  results  there  must  be  many 
presentations  of  ideas  and  idea  groups.  But  this  is 


MENTAL   ACTIVITY  75 

largely  the  work  of  Illustration,  and  will  be  dealt  with 
in  later  chapters. 

In  addition  to  the  Laws  of  Thought  as  Thought  and 
the  various  laws  of  association  with  which  we  have 
dealt,  there  is  another  law  of  greater  generality  and  of 
fundamental  importance  in  the  art  of  Exposition. 
It  is,  in  fact,  the  ultimate  impulse  to  mental  activity, 
the  equivalent  in  the  mind  to  gravitation  in  the  mate- 
rial world.  It  may  be  called  the  Law  of  Mental  Har- 
mony. The  ideas  within  the  mind  must  be  at  peace 
with  each  other.  The  moment  friction  arises  there 
must  be  ceaseless  activity  till  the  disagreement  is 
removed.  Consistency  among  the  ideas  is  an  essential 
to  mind.  All  the  mental  content  must  be  harmonised; 
there  must  be  no  contradiction  in  the  arrangement 
that  has  been  imposed  upon  the  ideas.  It  does  not,  of 
course,  follow  that  each  mind  must  be  able  to  resolve 
all  the  contradictions  that  occur  in  the  course  of 
thought,  but  the  mind  must  try  to  reconcile  them. 
This  is  of  its  very  nature,  and  the  necessity  is  not 
limited  to  the  intellectual  class.  The  mind  of  the  sav- 
age is  as  sensitive  to  the  need  for  internal  peace  as  is 
the  mind  of  the  savant.  On  the  other  hand,  the  uni- 
versality of  the  need  for  internal  peace  is  compensated 
for  by  the  varying  degrees  of  reconciliations  that  will 
satisfy  it.  What  the  savage  cannot  explain  in  terms 
of  science  he  can  in  terms  of  superstition.  In  fact  one 
of  the  main  functions  of  superstition  would  seem  to  be 
the  satisfaction  of  this  imperious  mental  need.  The 
invisible  wind  has  no  mouth  to  make  the  weird  moan- 
ings  that  disturb  him,  so  the  savage  is  impelled  to  get 
rid  of  this  apparent  contradiction  of  the  rest  of  his  ex- 
perience. Accordingly  he  personifies  the  wind  and 


76     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

thus  supplies  it  with  the  necessary  apparatus,  without 
rousing  any  further  difficulty.  At  later  stages,  it  is 
true,  the  latent  difficulties  appear,  and  the  more 
sophisticated  successor  of  the  savage  has  to  invent 
some  other  plausible  explanation.  The  mind  is  exact- 
ing in  its  demand  for  some  explanation  or  other; 
it  is  less  exacting  in  the  quality  of  the  explanation  it 
accepts. 

Herbert  Spencer  gives  an  interesting  account  of  the 
stages  by  which  he  arrived  at  what  he  considered  to  be 
the  truth  1  about  the  colour  of  shadows.  At  the  first 
stage  he  regarded  them  as  black,  since  he  had  been  ac- 
customed to  use  India  ink  to  represent  them  in  his 
drawings.  At  eighteen  he  was  told  by  a  friend  that  all 
shadows  are  neutral  tint,  but  "it  was  only  after  my 
friend  had  repeatedly  drawn  my  attention  to  instances 
in  nature,  that  I  finally  gave  in."  He  held  the  neutral- 
tint  view  for  some  years,  though  he  did  observe  "that 
the  tone  of  the  neutral  tint  varied  considerably  in  dif- 
ferent shadows."  The  divergences,  however,  "were 
not  such  as  to  shake  my  faith  hi  the  dogma."  His 
peace  of  mind  was  at  last  disturbed  by  a  statement  in 
a  popular  work  on  Optics:  "the  colour  of  a  shadow  is 
always  the  complement  of  the  colour  of  the  light  casting 
it."  He  wanted  to  know  "  Why  are  shadows  coloured? 
and  what  determines  the  colour?"  As  a  result  of  his 
investigations :  — 

"It  became  manifest  that  as  a  space  in  shadow  is  a  space  from 
which  the  direct  light  alone  is  excluded,  and  into  which  the  indirect 
light  (namely,  that  reflected  from  surrounding  objects  by  the  clouds 
and  sky)  continues  to  fall,  the  colour  of  a  shadow  must  partake  of  the 
colour  of  everything  that  can  either  radiate  or  reflect  light  into  it. 

»  "The  Valuation  of  Evidence,"  Essays  (1891),  Vol.  II,  p.  161. 


MENTAL  ACTIVITY  77 

Hence  the  colour  of  a  shadow  must  be  the  average  colour  of  the  diffused 
light;  and  must  vary,  as  that  varies,  with  the  colours  of  all  surround- 
ing things.  Thus  was  at  once  explained  the  inconstancy  I  had  al- 
ready noticed ;  and  I  presently  recognised  in  Nature  that  which  the 
theory  implies  —  namely,  that  a  shadow  may  have  any  colour 
whatever,  according  to  circumstances. 

"  Here,  then,  respecting  certain  simple  phenomena  that  are  hourly 
visible,  are  three  successive  convictions ;  each  of  them  based  on  years 
of  observation ;  each  of  them  held  with  unhesitating  confidence ; 
and  yet  only  one  —  as  I  now  believe  —  true." 

Further,  the  mind  does  not  go  out  of  its  way  to  seek 
for  troublesome  inconsistencies.  So  long  as  no  ques- 
tions are  raised  it  is  quite  content  to  accept  things  as 
they  are.  A  teacher,  giving  a  lesson  to  a  young  class 
on  a  bluebottle,  asked  how  the  creature  made  its  famil- 
iar buzzing  noise.  When  she  received  an  answer,  she 
told  the  children  that  she  expected  that  answer.  Of 
course  they  thought  the  bluebottle  buzzed  with  its 
mouth  because  when  they  wanted  to  buzz  they  did  it 
with  their  mouths.  Accepting  the  teacher's  word  that 
they  were  wrong,  the  class  had  no  peace  till  she  told 
them  that  the  buzzing  was  caused  by  the  wings.  This 
gave  the  children  perfect  satisfaction,  as  it  did  the 
teacher,  till  her  Normal  Master  pointed  out  that  if 
you  remove  the  bluebottle's  wings,  it  does  not  stop 
buzzing,  but  actually  buzzes  a  little  harder  than  usual. 
It  was  now  the  teacher's  turn  to  be  worried,  and  it  was 
not  till  she  had  learned  about  the  special  little  buzzing 
organ  l  that  she  could  drop  the  subject  and  be  at  peace 
once  more. 

Every  mind  contains  a  large  number  of  contradic- 
tions that  give  rise  to  no  trouble  because  they  are  not 

'Discovered  by  Landois.  T.  H.  Huxley:  Anatomy  of  Inverte- 
brated  Animals,  p.  377. 


78     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

perceived.  The  two  sets  of  facts  lie  apart,  and  are 
never  brought  into  contact  with  each  other,  so  the  mind 
is  content  with  its  erroneous  correlation.  It  was  an 
experienced  M.D.  with  a  tincture  of  literature  who  con- 
fessed that  he  had  just  discovered  the  true  meaning  of 
a  " flash  in  the  pan."  He  had  all  along  associated  the 
proverb  with  the  frying  pan.  He  knew  quite  as  much 
about  flintlocks  as  about  frying  pans,  but  he  had  never 
had  occasion  to  connect  the  proverb  with  the  firearm. 
The  same  sort  of  thing  is  seen  in  relation  to  our  precepts 
of  religion  and  of  business.  We  usually  keep  them 
carefully  apart.  Indeed  it  is  the  business  of  the  earnest 
and  faithful  clergyman  to  bring  face  to  face  the  pre- 
cepts from  the  two  spheres  and  ask  his  congregation  to 
reconcile  them.  His  success  is  measured  by  the  degree 
of  discomfort  he  is  able  to  introduce  into  the  minds  of 
his  hearers.  So  soon  as  he  has  introduced  dispeace 
among  the  elements  of  the  mental  content  he  has  pro- 
duced a  disturbance  that  cannot  be  set  at  rest  till  in 
some  way  or  other  the  exposed  contradiction  is  recon- 
ciled. No  doubt  churchgoers  are  often  very  successful 
in  effecting  a  superficial  reconciliation,  but  this  must  be 
honestly  satisfactory  so  far  as  it  goes,  if  the  person 
affected  is  to  get  any  peace. 

There  is  no  such  thing  as  deliberate  self-deception  in 
our  attempts  to  restore  harmony  between  apparent 
contradictions.  The  wish  no  doubt  is  often  father  to 
the  thought,  but  in  the  cases  we  have  in  view  the  con- 
tradiction is  assumed  to  have  been  brought  to  light  and 
placed  clearly  before  the  consciousness,  so  that  the  wish 
cannot  generate  the  thought,  much  as  the  mind  may 
desire  it.  When  Shakespeare  says  of  the  false  Duke 
Antonio,  — 


MENTAL  ACTIVITY  79 

"Who  having  unto  truth,  by  telling  of  it, 
Made  such  a  sinner  of  his  memory, 
To  credit  his  own  lie,  —  he  did  believe 
He  was  indeed  the  duke,"1 

he  is  describing  what  Antonio  would  have  "liked  to 
believe,  rather  than  what  he  did  believe.  No  doubt 
the  usurper  was  full  of  arguments  to  justify  himself 
in  ousting  his  brother,  and  these  arguments  probably 
gave  him  a  great  deal  of  consolation,  but  they  could 
never  convince  him  that  "he  was  indeed  the  duke." 
As  a  matter  of  fact  the  greater  the  efforts  he  made  to 
deceive  himself,  the  less  likely  would  he  be  to  attain 
his  end,  for  he  would  only  be  keeping  more  prominently 
before  consciousness  the  contradiction  that  he  wished 
to  remove.  In  his  efforts  to  deceive  himself  he  would 
be  doing  what  the  good  expositor  is  continually  doing 
when  he  seeks  to  break  up  a  false  combination  of  ideas 
in  order  to  substitute  a  true  one.  For  this  co-presen- 
tation in  consciousness  of  ideas  that  are  really  con- 
tradictory to  each  other  is  an  essential  part  of  the 
process  of  Exposition.  It  may  be  called  Confrontation, 
since  it  implies  the  bringing  face  to  face  of  ideas  that 
cannot  live  peaceably  together. 

In  Confrontation  it  is  assumed  that  both  terms  of 
the  contradiction  are  known  to  the  person  concerned. 
If  this  is  not  the  case,  no  real  confrontation  can  take 
place.  I  once  tried  to  prove  to  an  Arran  farmer  that 
the  earth  is  round.  I  did  not  succeed.  He  was  in  the 
wrong,  no  doubt,  but  his  was  a  mind  of  the  most  vigor- 
ous kind,  a  mind  that  worked  admirably  within  its 
limits.  These  limits  excluded  all  the  scientific  ideas 
that  make  it  necessary  to  believe  that  the  earth  is 

1  The  Tempest,  Act  I,  Sc.  2. 


80     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

round.  All  the  ideas  that  had  access  to  the  farmer's 
mind  were  on  the  most  friendly  terms  with  all  the  other 
ideas  to  be  found  there.  So  soon  as  anyone  is  able  to 
introduce  into  that  man's  mind  an  idea  that  is  incon- 
sistent with  the  flatness  of  the  earth,  a  disturbance  will 
be  set  up  that  may  lead  to  the  true  arrangement  of  his 
ideas  on  this  subject,  but  is  more  likely  to  lead  to  a  rear- 
rangement which  shall  explain  the  particular  inconsis- 
tency of  which  he  has  been  made  conscious,  without 
necessarily  corresponding  with  what  we  call  fact. 

The  principle  of  Confrontation  is  nowhere  better 
illustrated  than  in  the  Socratic  method.  It  was  the 
custom  of  Socrates  to  begin  his  discussions  by  a  demand 
for  a  definition,  which  in  his  ironical  way  he  often  rep- 
resented to  be  a  help  to  himself  in  getting  at  the  true 
meaning  of  the  subject  under  discussion.  It  was  not 
long  before  he  proceeded  to  confront  the  ideas  put  for- 
ward by  his  interlocutor  with  certain  other  ideas  that 
he  knew  formed  a  part  of  that  interlocutor's  mental 
content.  The  opposition  thus  disclosed  gave  an  excel- 
lent opportunity  of  stimulating  that  enquiry  that  was 
always  Socrates'  aim.  The  method,  in  fact,  has  almost 
always  three  stages.  First  there  is  confidence  without 
proper  foundation;  next  as  the  result  of  Confrontation 
there  arises  doubt  and  desire  to  attain  to  the  truth; 
then  in  the  third  place  comes  certainty  founded  on 
legitimate  grounds.  It  is  true  that  in  some  of  the 
actual  Socratic  dialogues  the  third  stage  is  not  attained, 
the  master  contenting  himself  with  the  disturbance 
that  he  had  set  up,  well  knowing  that  the  interlocutors 
could  not  settle  down  till  they  had  reached  some  sort 
of  conclusion,  which  if  not  perhaps  so  satisfactory 
as  one  that  could  have  been  supplied,  had  at  any 


MENTAL  ACTIVITY  81 

rate  the  compensating  advantage  of  having  been  at- 
tained by  the  effort  of  the  thinker  himself.  This 
method  of  unfinished  exposition  may  be  permissible  in 
the  case  of  advanced  pupils,  but  with  the  ordinary 
schoolboy  it  is  generally  better  to  carry  the  dialogue 
to  its  legitimate  conclusion.  The  work  of  the  ordinary 
school  affords  many  opportunities  to  apply  the  method 
of  Confrontation. 

To  illustrate,  take  the  case  of  that  constant  diffi- 
culty at  the  early  stages  of  composition,  the  incomplete 
sentence.  Pupils  brought  up  in  illiterate  homes  are 
very  apt  to  make  a  relative  clause  stand  by  itself, 
with  no  other  help  than  the  original  grammatical  sub- 
ject. In  schools  where  the  pupils  come  from  homes 
in  which  grammatical  English  is  habitually  spoken,  there 
is  not  so  much  danger  of  this  particular  form  of  error, 
but  every  teacher  in  a  school  for  the  poorer  classes  is 
unpleasantly  familiar  with  such  a  sentence  in  a  pupil's 
exercise  book  as  — 

John  who  broke  the  window 

The  following  is  a  verbatim  reproduction  of  a  lesson 
actually  given  to  a  class  of  about  sixty-five  rather  dull 
boys  of  average  age  11J.  The  sentence  had  occurred 
in  one  of  the  class  exercise  books,  and  was  placed  on  the 
blackboard,  as  it  had  been  written,  with  the  addition 
of  a  comma  after  the  word  John.1 

1  The  class  had  gone  through  a  regular  course  of  instruction  on  the 
nature  of  the  sentence,  and  knew  in  theory  all  about  sentence  making, 
and  the  distinction  between  a  sentence  and  a  mere  phrase.  The  pur- 
pose of  the  lesson,  therefore,  was  not  so  much  to  communicate  new 
ideas  as  to  give  a  meaning  to  ideas  already  known,  and  to  increase 
their  presentative  activity  by  co-presenting  them  to  the  consciousness 
in  their  proper  connections. 
G 


82     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

Teacher.  Now  what  did  John  do  ? 
Pupil  (confidently).     Broke  the  window. 
T.  Then  what  did  who  do  ? 
P.  Broke  the  window. 
T.  Were  there  two  windows,  then  ? 
P.   No,  sir. 

T.  Then  who  broke  it  ? 
P.  John. 

T.   And  what  did  who  do? 

P.   (doubtfully).  It  says  '  who  broke  the  window.' 
T.  Did  it  take  two  to  break  the  window? 
P.   No,  sir. 

T.  Then  which  of  them  did  the  breaking  ? 
(Pupils  puzzled.   No  answer.) 
T.   How  many  people  were  there  altogether  ? 
P.    (cautiously).   John  and  who. 
T.  Now,  which  was  bigger,  John  or  who  t 
P.  They're  both  the  same. 
T.  Then  there  was  only  one  person  there  ? 
P.   Yes,  sir. 

T.  And  what  was  his  name  ? 
P.  John. 

T.  And  what  did  he  do  ? 
P.  Broke  the  window. 

T.  Then,  would  it  not  be  enough  to  say, '  John  broke  the  window '  ? 
P.  Yes,  sir. 

T.  Is  that  what  it  says  on  the  blackboard  ? 
P.   No,  sir:  it  says,  'John,  who  broke  the  window.' 
T.   And  John  and  who  are  the  same  person  ? 
P.  Yes,  sir. 

T.  Then,  they  both  have  the  same  right  to  the  verb  ? 
P.  Yes,  sir. 

T.  Which  of  them  is  nearer  the  verb  ? 
P.   Who. 

T.   What  mark  is  between  John  and  the  verb  ? 
P.  A  comma. 

T.   Now  if  only  one  of  the  two  can  claim  the  verb,  which  has  the 
better  right  to  it  ? 
P.   Who. 


MENTAL  ACTIVITY  83 

T.  And  every  noun  and  pronoun  that  is  a  subject  must  have  a 
verb? 

P.  Yes,  sir. 

T.  Then  if  who  gets  '  broke,'  what  verb  is  left  for  John  f 

P.  None. 

T.  How  many  subjects  are  there  here  ? 

P.  Two. 

T.  And  how  many  verbs? 

P.  One. 

T.  And  every  subject  must  have  a  verb  ? 

P.  Yes,  sir. 

T.  How  many  verbs  do  we  need,  then,  besides  'broke '? 

P.  One. 

71.  Give  me  one. 

(No  answer.) 

T.  John  (who  broke  a  window)  did  something,  or  was  something. 
What  would  you  do  if  you  broke  a  window  ? 

P.  (promptly) .  Run  away,  sir.1 

T.  Finish  it,  then.     John,  who  broke  a  window ? 

P.  Ran  away. 

T.  Which  are  the  two  verbs  now  ? 

P.  'Broke 'and 'ran.' 

T.  Which  belongs  specially  to  who  f 

P,  Broke. 

T.  And  to  John? 

P.  Ran. 

In  this  and  in  all  other  applications  of  the  Socratic 
method  the  teacher  is  really  leading,  though  he  seems 
to  be  following.  He  knows  from  the  beginning  the  goal 
he  desires  to  reach.  He  knows,  further,  the  ideas  the 
pupil  already  possesses,  and  feels  that  it  is  his  business 

1  In  the  actual  lesson  this  answer  led  to  the  inevitable  moral  rebuke 
from  which  the  teacher  returned  to  the  main  subject  as  above.  As  a 
matter  of  fact  the  teacher  was  severely  criticised  for  not  substituting 
in  the  final  part  the  moral  "  paid  for  it, "  instead  of  the  discreditable 
"ran  away."  It  does  seem  a  pettifogging  distinction,  but  I  am  in- 
clined to  think  the  critics  are  right. 


84     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

so  to  manipulate  those  ideas  that  they  shall  ultimately 
form  the  combinations  he  desires. 

But  when  we  say  that  the  pupil  possesses  certain 
ideas,  we  do  not  mean  that  these  ideas  are  necessarily 
present  in  the  consciousness  of  the  pupil  when  the  les- 
son begins.  At  any  moment  in  a  given  mind  only  a 
very  limited  number  of  ideas  can  be  functioning.  The 
mind  is  capable  of  being  conscious  in  a  great  variety  of 
ways,  but  is  not  capable  of  being  conscious  in  all  those 
ways  at  one  and  the  same  moment.  When  we  say  that 
a  mind  possesses  a  certain  idea,  we  mean  that  that  mind 
has  a  permanent  potentiality  of  acting  uniformly  under 
certain  identical  conditions  as  often  as  those  conditions 
recur.  An  idea  not  in  consciousness  may  therefore 
be  regarded  as  a  permanent  possibility  of  appropriate 
response  to  certain  stimuli. 

The  field  of  consciousness  is  limited,  and  unless  an 
idea  happens  to  be  within  that  field  at  a  given  moment 
it  would  seem  to  be  powerless,  and  indeed  practically 
as  if  it  did  not  exist.  While  we  are  thinking  at  this 
moment  about  consciousness  and  activity,  myriads  of 
ideas  that  in  ordinary  speech  we  may  be  said  to  possess 
are  lying  dormant,  and  exercise  no  influence  upon  the 
ideas  that  are  at  present  in  consciousness.  Our  ideas 
about  rock  crystals,  for  example,  are  as  if  they  had  no 
existence.  But  the  important  point  has  to  be  consid- 
ered :  Are  all  our  ideas  that  are  not  within  consciousness 
at  a  particular  moment  equally  inert?  When  a  man  is 
thinking  of  the  power  of  ideas,  for  example,  are  his 
ideas  about  rock  crystals  and  his  ideas  about  John 
Locke  equally  ineffective  ?  He  is  not  thinking  about 
either  Locke  or  crystals,  but  we  have  the  general  feel- 
ing that  Locke  is  nearer  to  his  thoughts  at  the  present 


MENTAL  ACTIVITY  85 

moment  than  are  the  crystals.  Though  Locke  is  below 
the  threshold  of  consciousness  he  somehow  seems  nearer 
that  threshold  than  do  the  crystals.  Is  there  then  a 
differentiation  among  the  ideas  that  are  out  of  con- 
sciousness corresponding  to  the  differentiation  we  have 
seen  to  maintain  within  consciousness?  It  would 
seem  that  between  the  conscious  and  the  unconscious 
there  is  a  clear  dichotomy.  We  are  either  conscious 
of  an  idea  or  we  are  not;  anything  that  is  below  the 
threshold  is  therefore  out  of  consciousness.  Perhaps 
our  trouble  arises  from  a  too  rigid  application  of  our 
figure  of  the  threshold.  There  is  something  extremely 
definite  in  the  idea  of  a  threshold.  A  visitor  either  has 
or  has  not  crossed  it.  He  is  either  in  our  house  or  he 
is  not.  But  if  we  are  expecting  him,  or  if  we  chance  to 
see  him  coming  up  the  walk  we  are  influenced  by  him 
before  he  is  actually  in  the  house.  The  figure  is  not 
perhaps  a  very  illuminating  one,  as  it  amounts,  after  all, 
to  an  illustration  of  consciousness  by  an  appeal  to  con- 
sciousness. But  since  it  is  impossible  to  transcend 
consciousness,  it  is  difficult  to  see  how  this  community 
of  subject-matter  can  be  avoided. 

Even  if  we  could  justify  the  rigidity  of  the  threshold 
figure,  there  would  still  remain  a  certain  vagueness 
about  the  mental  content  in  the  marginal  area.  Ideas 
are  in  constant  motion  about  the  threshold  of  conscious- 
ness :  now  on  the  line,  now  above,  now  below.  An  idea 
that  is  at  the  present  moment  below  the  threshold,  but 
a  moment  ago  was  above  it  and  in  another  moment  will 
be  above  it  again,  may  be  said  to  exercise  a  certain 
influence  on  the  continuum  on  the  borders  of  which  it 
wavers.  It  is  to  meet  cases  of  this  kind  that  the  term 
subconscious  is  used.  Of  course  an  idea  must  either 


86     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

be  in  consciousness  or  not;  accordingly  we  must  regard 
a  subconscious  idea  as  in  some  way  or  other  within 
consciousness.  Yet  from  the  way  in  which  the  term 
is  used  one  would  almost  be  led  to  think  that  it  meant 
that  certain  ideas  are  in  the  consciousness  without  our 
being  conscious  of  them  —  a  clear  contradiction  in 
terms.  By  the  Law  of  Excluded  Middle  there  seems 
to  be  no  place  for  the  subconscious  between  the  con- 
scious and  the  unconscious.  Yet  it  is  obvious  that 
there  is  a  difference  between  an  idea  that  is  hovering 
on  the  verge  of  consciousness,  and  one  that  is  lost  in 
the  limbo  of  unconsciousness  and  may  never  again 
return  to  consciousness.  Logic  may  rule  out  the  sub- 
conscious, but  Psychology  must  find  it  a  place. 

To  begin  with,  it  has  to  be  admitted  that  ideas  that 
are  not  present  hi  the  consciousness  exercise  a  certain 
influence  upon  ideas  that  are  in  the  consciousness,  and 
if  an  absolute  distinction  is  demanded,  it  may  be  satis- 
factorily put  for  practical  purposes  as :  At  any  given 
moment  an  idea  may  be  said  to  be  subconscious  if 
without  being  itself  within  the  consciousness  it  exercises 
an  influence  on  ideas  that  are  at  that  moment  within 
the  consciousness.  It  is  easy  to  see  that  an  idea  that 
has  just  left  the  consciousness  may  leave  behind  it  an 
influence  that  does  not  cease  the  moment  it  passes  over 
the  threshold.  So  with  an  idea  that  is  coming  up 
towards  consciousness,  it  may  not  be  very  difficult  to 
persuade  people  that  it  may  cast  its  influence  before  it, 
and  thus  to  some  extent  act  within  the  mind  before  it 
appears.  But  we  must  go  further,  and  admit  that  ideas 
may  exercise  an  influence  within  the  mind  even  if  they 
do  not  reach  the  consciousness  at  all  on  the  particular 
occasion  that  we  examine.  When  we  are  dealing  with  a 


MENTAL  ACTIVITY  87 

difficult  and  complicated  problem,  for  example,  we  call 
into  the  consciousness  a  large  number  of  relevant  ideas 
and  carefully  examine  them  in  relation  to  each  other, 
and  to  the  problem  we  are  working  with.  But  as  we 
shall  see  more  fully  later1  we  cannot  at  will  recall  all 
the  relevant  ideas.  By  skilful  manipulation  we  may 
gather  together  most  of  the  significant  ideas,  but  some 
at  least  remain  outside  consciousness.  Are  these  un- 
called witnesses  without  influence  on  our  decisions  ? 
The  answer  would  appear  to  be  that  ideas  in  the  sub- 
conscious region  do  exercise  an  influence  upon  ideas 
within  consciousness,  even  though  on  the  occasion  in 
question  they  do  not  emerge  at  all  above  the  threshold. 
The  mind  is  dealing  with  a  knotty  problem  in  some 
such  dangerous  subject  as  Political  Economy  —  noted 
for  its  pitfalls.  The  ideas  at  present  in  the  continuum 
seem  to  fit  into  each  other  quite  naturally;  there  is 
therefore  internal  harmony,  and  the  problem  seems  to 
be  solved.  Yet  the  mind  is  not  satisfied.  It  has  an 
uneasy  sense  that  there  is  a  flaw  somewhere,  and  goes 
on  calling  up  all  the  available  ideas  connected  with  the 
subject  in  order  to  discover  some  possible  error.  For 
long  nothing  adverse  turns  up ;  but  by  and  by  an  idea 
rises  above  the  threshold  and  breaks  down  the  hypoth- 
esis that  was  in  all  other  respects  satisfactory.  This 
belated  idea  may  be  reasonably  supposed  to  be  sub- 
conscious at  the  time  that  the  hypothesis  was  formed, 
thus  causing  the  disquieting  vague  impression.  Fur- 
ther it  would  have  been  none  the  less  subconscious  even 
if  it  had  not  come  up  in  time  to  break  down  our  hypoth- 
esis, or  had  never  come  into  the  consciousness  at  all. 
It  might  quite  well  have  caused  the  uncomfortable 

1  P.  104. 


88     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

feeling  in  the  mind  without  coming  up  in  time  to  warn 
the  thinker.  When  the  thinker's  critics  point  out  the 
flaw,  the  subconscious  idea  rises  into  consciousness 
and  the  thinker  recognises  that  it  had  given  him  a 
vague  warning  though  it  did  not  reach  his  conscious- 
ness in  tune  to  prevent  the  blunder. 

The  phenomena  of  the  subconscious  may  be  readily 
correlated  with  certain  of  the  theories  of  brain  action. 
If  the  associations  formed  among  ideas  correspond  to 
interrelations  established  among  certain  neural  systems 
through  their  functioning  in  a  systematic  way  hi  re- 
sponse to  certain  stimuli,  it  may  well  be  assumed  that 
when  certain  systems  are  stimulated  to  the  necessary 
extent,  certain  corresponding  ideas  rise  into  the  con- 
sciousness. This  stimulation  has  the  natural  tendency 
to  spread  among  the  other  systems,  but  naturally  it  will 
spread  more  easily  among  systems  correlated  with  ideas 
that  have  formerly  been  connected  with  the  ideas  at 
present  in  consciousness.  It  may  plausibly  be  sug- 
gested that  within  the  brain  there  is  a  sort  of  physical 
replica  of  the  field  of  consciousness;  certain  neural 
systems  are  in  a  high  state  of  excitement  —  these  cor- 
respond to  the  focal  ideas.  Systems  in  various  de- 
creasing degrees  of  excitement  may  well  correspond  to 
the  various  degrees  of  obscuration  of  the  ideas  till 
tracts  are  reached  that,  though  stimulated  by  the  gen- 
eral impulse  that  affects  all  the  system  we  are  dealing 
with,  are  not  sufficiently  stimulated  to  cause  a  definite 
idea  to  rise  into  consciousness.  Such  tracts  will  corre- 
spond to  the  ideas  that  are  in  the  subconscious  state. 
If  the  neural  system  concerned  is  thoroughly  well 
organised,  as  must  be  the  case  with  regard  to  the  sys- 
tem that  regulates  our  thinking  on  any  subject  of  which 


MENTAL  ACTIVITY  89 

we  have  an  intelligent  knowledge,  it  will  be  impossible 
to  stimulate  some  of  the  tracts  up  to  consciousness 
pitch  without  at  the  same  time  stimulating  all  the  cor- 
related tracts  into  some  degree  of  activity.  Accord- 
ingly, even  the  most  remote  relevant  ideas  will  be  raised 
to  at  least  the  subconscious  state,  and  the  whole  system 
so  energised  that  its  elements  require  only  a  very  slight 
additional  impulse  to  send  them  up  into  consciousness. 

This  additional  stimulus  is  what  we  seek  to  give  them 
by  our  ordinary  methods  of  dealing  with  problems. 
We  put  ourselves  in  the  way  of  stimulating  certain 
ideas.  We  turn  to  books  where  we  know  such  ideas  are 
treated.  This  gives  us  the  primary  set  of  ideas.  The 
systems  corresponding  to  these  primary  ideas  stimu- 
late a  great  many  other  systems  at  the  secondary  and 
tertiary  degrees  of  remoteness.  If  our  system  of  ideas 
is  perfectly  coordinated,  then  the  neural  tracts  will 
inevitably  be  stimulated  in  their  proper  order  and  the 
corresponding  ideas  will  present  themselves  to  con- 
sciousness, just  as  they  are  required  for  purposes  of 
thought.  This  indeed  is  what  happens  in  well-regulated 
minds  when  dealing  with  subjects  in  which  they  are 
quite  at  home. 

It  goes  without  saying  that  this  parallelism  between 
the  physical  and  the  mental  in  no  way  commits  us  to 
materialism.  Even  if  we  could  correlate  every  idea 
that  passes  through  the  mind  with  a  definite  corre- 
sponding cell  in  the  brain,  we  would  be  no  nearer  than 
we  were  before  to  the  solution  of  the  problem  of  the 
relation  between  mind  and  matter.  The  physical 
parallel  has  been  introduced  here  mainly  because  it  gives 
a  certain  confirmation  of  the  view  taken  with  regard  to 
the  place  of  the  subconscious  in  mental  process.  If 


90     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

the  theory  adopted  with  regard  to  the  subconscious 
fits  in  with  the  hypotheses  of  certain  physiological 
psychologists,  there  is  the  greater  likelihood  of  its 
being  true.  In  any  case  the  analogy  serves  as  a  useful 
illustration,  and  after  all,  if  analogy  is  not  always  itself 
a  reliable  argument,  we  are  told  that  it  often  indicates 
that  a  reliable  argument  exists. 


CHAPTER  IV 

MENTAL  BACKGEOUNDS 

PAINTERS  are  familiar  with  the  phenomena  of  what 
they  call  Turbid  Media.  Colours  vary  according  to  the 
colour  tone  of  the  material  upon  which  they  are  laid. 
This  is  what  the  Hon.  John  Collier  has  to  say  on  the 
subject:  — 

"  Rub  a  little  ivory  black  thinly  over  a  white  canvas,  it  will  ap- 
pear a  distinct  brown ;  mix  the  same  colour  with  white,  it  becomes 
a  neutral  grey ;  brush  this  grey  thinly  over  a  black  ground,  it  will 
have  a  distinctly  bluish  tinge ;  so  that  the  same  pigment  can  vary 
from  a  warm  brown  to  a  blue  grey  without  admixture  with  any 
other  colour  but  white,  merely  in  accordance  with  the  manipulation 
it  receives.  Yellow  ochre  gives  similar  results ;  when  lightly  brushed 
over  a  white  ground  it  seems  a  rich  orange,  when  brushed  in  pre- 
cisely the  same  way  over  a  black  ground  it  seems  a  sort  of  green." 

So  with  the  mind.  The  same  idea  has  to  harmonise 
itself  with  quite  a  different  tone  according  to  the  nature 
of  the  background  against  which  it  is  projected.  The 
groups  of  ideas  that  give  body  to  the  stream  of  con- 
sciousness may  be,  without  too  violent  a  figure,  com- 
pared with  a  background,  which  like  every  other  back- 
ground has  a  powerful  influence  on  our  view  of  any 
element  worked  into  the  foreground.  Naturally  the 
analogy  is  more  complete  when  we  deal  with  the  af- 
fective aspect  of  thought  or  speech.  Public  orators 
of  a  sentimental  turn  are  not  uncommonly  guilty  of 

1  Primer  of  Art,  p.  59. 
91 


92     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

falling  into  a  rhapsodical  mode  of  expression,  a  sort  of 
"Ah!"  strain,  that  renders  them  blind  to  the  real  mean- 
ing of  the  ideas  they  use.  The  emotional  background 
is  too  strong  for  the  ideas  that  are  projected  against  it. 
Next  morning  in  cold  blood  the  orator  usually  sees  his 
mistake;  indeed  there  is  a  danger  that  the  cold  daylight 
criticism  may  go  too  far  in  the  other  direction,  for 
it  has  always  to  be  remembered  that  there  are  occa- 
sions when  the  value  of  an  idea  must  not  be  judged  too 
closely  by  the  logical  standard.  Still  there  is  some- 
thing wrong  when  the  emotional  background  retains 
its  paralysing  power  even  through  the  callous  period 
of  proofreading.  The  following  occurs  at  the  end  of  a 
sermon-tale  to  children  by  a  well-known  London  clergy- 
man, who  published  it  along  with  other  sermons  in 
book  form  in  1891. 

"And  away  down  in  81st  Street  a  woman  was  stitching  what 
seemed  like  a  little  nightgown,  but  ah  me !  it  was  not  that  —  it  was 
something  sadder  still,  for  her  little  dear  baby  had  died ;  and  the 
mother's  heart  was  full,  and  the  tears  would  flow." 

Apart  from  the  background  of  this  sad  sermon-tale 
no  one  would  think  that  "a  little  nightgown"  was  a 
particularly  sad  object,  only  less  sad,  hi  fact,  than  a 
little  shroud.  Yet  so  powerful  is  this  background  of 
sentiment,  that  not  only  did  it  blind  the  preacher  at  the 
time,  but  completely  deceived  two  different  classes  of 
divinity  students  to  whom  I  had  occasion  to  lecture, 
and  upon  whom  I  took  the  liberty  to  experiment. 
My  subject  was  the  preparation  of  sermons  for  the 
young,  and  I  read  the  passage  —  naturally  beginning  a 
little  bit  before  the  dangerous  passage  in  order  to  give 
the  background  its  proper  effect  —  to  illustrate  a 
psychological  principle.  In  both  cases  the  implicit 


MENTAL  BACKGROUND  93 

absurdity  escaped  detection,  though,  when  it  was 
pointed  out  to  them,  the  young  men  were  much  cha- 
grined that  they  had  allowed  it  to  pass. 

But  the  figure  of  a  background  in  mental  matters 
is  not  limited  to  the  affective  tone.  It  has  a  useful 
application  on  the  ideational  plane.  We  have  found 
that  each  idea  that  occurs  to  the  mind  must  make  itself 
at  home  there.  It  must  harmonise  itself  with  its  sur- 
roundings; and  must  take  a  different  meaning  accord- 
ing to  the  mental  background  against  which  it  is  pro- 
jected. The  presented  content  may  be  quite  neutral 
or  it  may  have  a  positive  tone  of  its  own.  In  both  cases 
the  new  idea  or  ideas  must  submit  to  a  modification  of 
tone  or  meaning  from  the  effect  of  the  background. 

Take  some  such  colourless  sentence  as  Think  of  him, 
and  note  the  difference  effected  by  projecting  it  against 
the  following  backgrounds. 

A  picture  in  Life  of  a  low-class  photographer  trying  to  encourage 
a  pleasant  expression  on  his  female  sitter's  face. 

A  widow  laying  flowers  on  a  grave  and  addressing  her  little  girl. 

A  religious  revival  meeting. 

A  French  schoolmaster  during  the  Franco- Prussian  war  pointing 
to  a  portrait  of  the  first  Napoleon. 

A  conspirators'  meeting  where  a  traitor's  name  has  been  men- 
tioned. 

A  crowd  of  starving  "unemployed  "  watching  the  Mayor  pass  from 
his  carriage  to  a  City  Banquet. 

The  same  thing  applies  to  an  idea  dealing  with  a  con- 
crete object,  say  a  fish.  Note  how  the  emotion  aroused 
varies  according  to  the  background.  Against  a  back- 
ground that  includes  the  Early  Christians  and  the 
Catacombs  it  arouses  either  a  deeply  religious  or  a 
mildly  antiquarian  interest.  Try  it  now  against  a 


94     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

background  of  Astronomy,  Sport,  Bread-winning, 
Geography,  Art,  Science,  Slang,  Heraldry,  Asceticism. 

Most  of  the  honest,  that  is,  unmalicious,  misunder- 
standings of  life,  are  the  result  of  failing  to  make  al- 
lowance for  the  background  in  the  mind  of  another. 
When  the  same  ideas  are  presented  against  different 
backgrounds,  the  consequent  confusion  is  so  inevitable 
that  common  speech  includes  a  special  phrase  to  ex- 
press this  particular  form  of  misunderstanding.  When 
people  are  at  "cross  purposes,"  they  are  dealing  with 
the  same  words  in  different  connections,  which  is  the 
same  as  saying  that  the  meanings  are  modified  by  the 
backgrounds.  Here  we  have  passed  beyond  mere  tone, 
and  have  reached  the  region  of  relation  among  the  ele- 
ments that  make  up  the  content  of  mind.  The  care- 
less, unreflective  man  takes  it  for  granted  that  the  idea 
he  sends  forth  from  a  given  background  will  find  a  cor- 
responding background  in  the  mind  of  his  hearer  or 
reader.  Fortunately  his  expectation  is  usually  justi- 
fied. By  the  very  fact  that  two  minds  are  in  com- 
munication, they  are  placed  in  such  a  relation  as  to 
encourage  the  development  of  the  same  backgrounds. 
But  at  the  very  beginning  of  a  conversation  there  is 
sometimes  a  little  difficulty.  The  preliminary  talk 
between  two  persons,  before  coming  to  the  real  point, 
is  a  sort  of  tuning  up,  a  kind  of  mental  feeling  for  the 
proper  pitch.  This  preliminary  talk  has  sometimes 
been  compared  to  the  few  passes  that  a  pair  of  fencers 
make  before  coming  to  the  real  business  of  the  en- 
counter. But  the  figure  of  finding  the  pitch  is  perhaps 
nearer  the  truth. 

Many  people  —  particularly  young  people  -  are 
irritated  at  what  they  call  "beating  about  the  bush." 


MENTAL  BACKGROUND  95 

No  doubt  the  principle  in  medias  res  is  admirable, 
if  we  are  sure  that  we  and  our  interlocutor  are  to  be  in 
the  middle  of  the  same  res.  If  two  men  meet  to 
discuss  the  same  subject,  they  are  probably  provided 
with  the  same  backgrounds,  or  at  any  rate  closely 
similar  backgrounds;  but  even  then  a  certain  amount 
of  harmonising  may  be  necessary.  It  is  quite  possible 
that  each  may  view  the  subject  against  a  background 
quite  differently  made  up,  though  composed  of  the 
same  elements.  People  who  argue  for  the  sake  of 
arguing,  people  who  write  to  the  newspapers,  almost  in- 
variably deal  with  ideas  in  the  light  of  their  own  back- 
grounds, and  refuse  to  take  the  trouble  to  discover  the 
mental  backgrounds  against  which  the  same  ideas  are 
projected  in  the  mind  of  the  person  with  whom  they 
debate.  If  we  desire  to  convince  another  person  that 
his  view  is  wrong,  we  must  endeavour  to  find  out  exactly 
what  that  view  is;  we  must  discover  what  sort  of  back- 
ground his  ideas  are  projected  against. 

The  reason  why  we  are  so  seldom  at  cross  purposes 
is  that  we  rarely  move  out  of  our  own  set.  All  societies 
are  made  up  of  sets  or  coteries,  each  of  which  is  marked 
by  the  possession  of  a  common  series  of  backgrounds. 
In  dealing  with  those  of  our  own  set  we  have  no  diffi- 
culty, and  dealing  with  our  own  set  makes  up  the 
greater  part  of  life  for  most  of  us.  It  is  when  we  have 
communication  with  our  political  opponents,  with 
members  of  a  different  church,  with  foreigners,  even 
with  members  of  some  of  the  ordinary  "  Anti"  societies, 
that  we  realise  that  our  ideas  do  not  seem  to  have  the 
effect  upon  our  interlocutors  that  we  intend. 

Teachers  in  a  more  or  less  conscious  way  feel  the 
need  of  bringing  their  own  backgrounds  into  harmony 


96     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

with  those  of  their  pupils.  Young  teachers  in  particu- 
lar soon  discover  that  their  questions  do  not  produce 
the  answers  they  were  intended  to  elicit.  A  question 
is  asked,  for  example,  the  answer  to  which  is  known 
to  be  within  the  range  of  the  pupil's  knowledge.  There 
is  no  doubt  about  the  matter.  The  teacher  knows,  from 
immediately  preceding  experience,  that  the  answer  is  in 
the  pupil's  mind  only  waiting  to  be  drawn  out.  Indeed 
the  question  may  be  fairly  regarded  as  nothing  more 
than  a  stage  in  the  process  of  making  clear  and  distinct 
an  idea  that  the  pupil  already  possesses,  though  in  a 
vague  way.  The  question  is,  however,  so  expressed  that 
the  pupil,  with  the  best  intention  in  the  world,  cannot 
discover  against  which  background  he  is  expected  to 
project  the  ideas  concerned.  Accordingly  he  projects 
them  against  the  first  available  background,  in  the  hope 
that  this  may  be  the  right  one. 

"Where  was  St.  Paul  converted?"  asks  the  teacher, 
speaking  from  a  geographical  background.  "In  the 
ninth  chapter  of  the  Acts,"  responds  the  pupil,  from 
a  background  of  textual  reference.  In  testing  the  in- 
telligence of  a  class  the  inspector  asks,  "Where  do  you 
find  gates?"  The  pupil,  from  a  background  made  up 
of  puzzling  experiences  of  the  Socratic  method,  answers: 
"We  don't  find  gates,  we  make  them."  From  an  his- 
torico-geographical  background  the  inspector  desired  to 
elicit  the  deleterious  effect  of  a  large  town  on  the  purity 
of  a  river.  He  brought  out  the  fact  that  Robert  the 
Bruce  spent  his  latter  years  at  Roseneath  on  the  Clyde 
in  Scotland,  and  that  as  a  recreation  he  very  probably— 
according  to  the  inspector  —  fished  in  the  river.  The 
question  that  was  to  incriminate  those  who  were  re- 
sponsible for  the  pollution  of  the  Clyde  took  the  form: 


MENTAL  BACKGROUND  97 

"Why  couldn't  the  Bruce  fish  there  now?"  From 
a  background  of  plain  common  sense  came  the  reply: 
"Because  he's  dead." 

It  is  manifest  that  what  we  are  here  calling  mental 
backgrounds  correspond  to  what  we  have  already 
spoken  of  as  continuums;  but  we  are  now  treating  them 
from  a  new  point  of  view.  Hitherto  we  have  been  con- 
cerned with  the  relative  clearness  or  obscurity  of  the 
elements  that  make  up  the  continuum;  now  we  are 
interested  in  the  varying  effects  of  the  same  idea  ac- 
cording to  the  continuum  in  which  it  is  found.  Instead 
of  considering  the  effect  of  the  diffusion  and  concentra- 
tion of  consciousness  on  the  composition  of  the  con- 
tinuum, we  now  examine  the  change  produced  on  a 
given  idea  by  the  company  in  which  it  finds  itself. 
The  management  of  mental  backgrounds  is  clearly 
an  important  part  of  the  process  of  Exposition:  ac- 
cordingly we  must  study  the  mechanism  of  these  back- 
grounds; we  must  look  into  the  problem  of  mental 
scene-shifting. 

With  regard  to  the  elements  out  of  which  the  back- 
grounds are  worked  up  there  is  probably  a  greater  uni- 
formity than  would  at  first  sight  be  expected.  The 
ultimate  elements,  the  products  of  sense-perception, 
are  practically  uniform,  though  no  doubt  even  here 
there  are  differences  corresponding  to  the  physical  con- 
ditions of  the  sense  organs.  But  even  admitting  the 
general  uniformity  of  elements  there  remains  a  vast 
possibility  of  differentiation  through  variety  in  com- 
bination. Given  a  hundred  minds  with  precisely  the 
same  ideas  as  presented  content,  it  is  probable  that  no 
two  of  them  have  the  ideas  arranged  in  the  same  way. 
The  order  in  which  the  ideas  were  originally  presented, 


98     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

and  the  circumstances  of  the  different  persons  con- 
cerned, have  brought  about  a  necessary  variety  in  the 
combinations.  It  is  obvious  that  it  is  impossible  to 
make  a  classification  of  minds  on  a  basis  of  mental  con- 
tent without  practically  attempting  to  "  exhaust  the 
universe,"  though  a  rough  and  ready  classification  may 
be  very  serviceable  for  practical  purposes.1  But  with 
respect  to  the  mechanism  by  which  combinations  are 
effected  there  need  not  be  the  same  difficulty.  Minds 
may  be  divided  into  three  classes  according  to  the 
degree  of  stability  they  establish  among  the  elements  as 
components  of  complexes.  Naturally  there  are  certain 
complexes  of  ideas  that  are  formed  to  correspond  to 
certain  complexes  of  objective  phenomena.  These 
complexes  owe  their  stability  to  the  uniformity  with 
which  they  react  satisfactorily  upon  the  conditions  of 
actual  experience.  But  certain  other  complexes  de- 
pend for  their  stability  .upon  the  quality  of  the  mind  in 
which  they  are  formed. 

From  this  point  of  view  the  first  kind  of  mind  may 
be  named  the  rigid.  It  is  marked  by  the  close  connec- 
tion that  is  maintained  among  the  elements  that  go  to 
form  a  given  background.  Instead  of  moving  freely 
among  themselves  the  individual  ideas  form  a  complex 
once  for  all,  and  can  hardly  be  separated  from  each 
other.  The  rigidity  may  result  from  the  emotional 
tone;  we  may  refuse  to  break  up  our  complex  because 
we  prefer  to  have  the  elements  arranged  in  that  way. 
This  is  the  case  with  the  stubborn  little  cottage  girl 

1  Such  studies  as  Dr.  Berthold  Hartmann's  Die  Analyse  des  kind- 
lichen  Gedankenkreises  als  die  naturgemdsse  Grundlage  des  ersten 
Schulunterrichts  (Leipzig,  1896)  show  that  a  good  beginning  has  al- 
ready been  made  in  this  kind  of  classification. 


MENTAL  BACKGROUND  99 

who  in  Wordsworth's  poem  refused  to  break  up  the 
combination  of  herself  and  her  brothers  and  sisters  into 
a  group  of  seven,  merely  because  two  of  them  were 
dead.  The  poet  does  his  best  to  break  up  the  com- 
plex: — 

" '  But  they  are  dead ;  those  two  are  dead ! 

Their  spirits  are  in  heaven ! ' 
Twas  throwing  words  away ;  for  still 
The  little  maid  would  have  her  will, 
And  said,  ' Nay,  we  are  seven  I'" 

The  extreme  case  of  this  rigidity  is  to  be  found  in  that 
form  of  insanity  that  bears  the  name  of  Videe  fixe. 

Very  frequently  the  natural  tendency  of  certain  minds 
towards  rigidity  is  intensified  by  bad  teaching,  teaching 
for  the  sake  of  immediate  results  rather  than  for  the 
sake  of  the  power  that  comes  from  the  organization  of 
ideas.  It  seems  to  save  time  to  present  ideas  in  ready- 
made  boluses.  Education,  however,  should  be  free  from 
the  trammels  of  such  time  conditions.  The  ultimate 
result  is  the  only  thing  worth  considering.  We  are  not 
here  concerned  with  the  practical  difficulties  of  supply- 
ing the  best  possible  equipment  for  life's  work  in  the 
limited  time  at  the  disposal  of  the  teacher  in  the  case 
of  the  average  child.  Few  questions  are  of  greater 
importance  than  that  of  making  the  most  of  the  short 
school  time  available  for  the  artisan  class.  But  at 
present  our  aim  is  to  get  at  the  best  ideal  state.  Once 
this  has  been  determined,  educators  may  be  in  a  posi- 
tion to  discuss  what  compromise,  as  a  compromise 
between  what  ought  to  be  and  what  is,  will  lead  to  the 
best  result.  Obviously  we  must  know  the  best  possible, 
before  we  can  examine  how  closely  we  can  approach  it 
without  attempting  to  overstep  the  limits  of  our  powers. 


100    EXPOSITION   AND   ILLUSTRATION   IN   TEACHING 

The  backgrounds  formed  by  rigid  minds  may  be 
termed  fixed.  Naturally  no  background  can  remain 
permanently  fixed,  except  perhaps  in  the  case  of  the 
insane,  but  in  ordinary  life  we  find  modified  forms  of 
I'idee  fixe.  Your  dull,  matter-of-fact  man  regards  all 
things  of  the  same  class  against  the  same  unvarying 
background.  He  finds  the  greatest  possible  difficulty 
in  knowing  what  nimbler- witted  people  mean.  The 
same  ideas  are  presented  to  him  and  to  them.  He  can- 
not understand  why  they  produce  such  a  different  effect 
in  the  two  cases. 

We  shall  see  later  that  up  to  a  certain  degree  of  elabo- 
ration, it  is  a  distinct  advantage  to  have  fixed  complexes 
of  ideas,  but  beyond  that  degree  fixity  is  a  thing  the 
teacher  must  fight  against.  In  the  case  of  rigid  minds  it 
is  obviously  of  prime  importance  that  the  first  presenta- 
tion of  a  given  complex  of  ideas  shall  be  properly  made, 
since  any  change  at  a  later  stage  will  be  exceedingly 
difficult.  To  prevent  the  evil  effects  of  rigidity,  then, 
the  best  means  is  to  present  the  component  elements  in 
as  simple  a  form  as  possible.  This  does  not  mean 
merely  in  the  easiest  forms,  but  as  nearly  as  may  be  in 
the  forms  resulting  from  ultimate  analysis.  The  mind 
we  appeal  to  ought  to  do  its  own  combinations.  It 
does  not,  of  course,  follow  that  the  mind  we  deal  with 
will  form  a  different  complex  from  that  we  have  our- 
selves formed.  The  skilful  teacher  will  in  fact  manipu- 
late his  facts  so  that  the  pupil  will  form  precisely  the 
same  complex  as  the  less  skilful  teacher  would  present 
as  a  ready-made  bolus.  But  the  fact  that  the  bolus-fed 
pupil  and  his  better-taught  compeer  form  the  same 
final  complex,  in  no  way  proves  that  the  resulting  know- 
ledge is  of  the  same  value  in  the  two  cases.  There  is  a 


MENTAL  BACKGROUND  101 

fundamental  psychological  difference  between  ideas 
grouped  by  the  mind  itself,  and  the  same  ideas  in  the 
same  grouping  when  that  grouping  has  been  presented 
ready  made  as  the  result  of  the  operations  of  another 
mind.  It  is  true  that  even  when  the  mind  has  made 
its  own  complexes  of  ideas,  there  may  be  unhealthy 
rigidity  in  the  result.  Some  minds  are  naturally  in- 
elastic. That  class  of  mind  that  Roger  Ascham  calls 
harde  wittes  l  is  inclined  to  be  unduly  rigid.  Great 
care  must  accordingly  be  taken  that  the  true  complex 
should  be  suggested  at  an  early  stage,  and  further, 
continual  exercise  should  be  given  in  dealing  with  the 
same  ideas  in  different  connections.  Exercises  of  all 
kinds  have  their  uses  in  this  way.  Every  time  that  the 
teacher  is  able  to  satisfy  the  reproach  that  is  implied  in 
the  complaint  "But  you  said  so-and-so, "  he  is  loosening 
the  too  rigid  bonds  that  unite  ideas. 

After  all,  harde  wittes  form  capital  material  for  the 
teacher  to  exercise  his  skill  upon,  and  it  is  not  difficult 
to  see  that  old  Roger  has  a  warm  side  to  this  class  of 
pupil.  But  every  teacher  dislikes  the  opposite  type  of 
mind  that,  for  want  of  a  better  name,  may  be  called  the 
fluid.  In  this  case  there  is  no  fear  of  too  close  a  con- 
nection among  the  ideas  that  form  a  background. 
They  are  allowed  to  roll  about  in  the  mind  pretty  much 
as  the  molecules  of  a  liquid  mingle  with  each  other. 
Some  complexes  must,  of  course,  be  maintained  in  a 
position  of  comparative  stability,  else  the  mind  would 
fall  to  pieces  altogether.  But  the  complexes  are  at  any 
time  easily  broken  up.  To  this  type  of  pupil  one  com- 
plex is  as  good  as  another.  But  even  here  we  must 

1  The  Scholemaster :  The  first  booke  teachyng  the  brynging  up  of 
youth.  Arber's  Reprints,  p.  34. 


102    EXPOSITION   AND  ILLUSTRATION   IN  TEACHING 

try  to  get  the  mind  to  do  its  own  combining  and  building 
up.  No  doubt  we  shall  have  to  use  stronger  induce- 
ments, and  we  must  find  better  and  firmer  bonds. 
Above  all  we  must  keep  on  repeating  those  connections 
that  we  seek  to  impress  on  the  pupil-mind.  Instead 
of  seeking  out  exercises  in  which  the  individual  ideas 
are  exhibited  in  different  connections  we  must  confine 
ourselves  to  those  that  illustrate  the  working  of  the 
ideas  in  the  same  connection  though  under  different 
aspects.  The  complex  must  as  before  be  made  by  the 
pupil  himself;  but,  once  made,  it  may  be  greatly 
strengthened  by  the  outside  influence  of  the  teacher. 

The  fixed  background  is  in  general  more  character- 
istic of  mature  life;  the  unstable  background  is  common 
in  school.  The  necessity  of  childhood  to  grow  as  well 
as  to  live  makes  it  imperative  that  material  for  growth 
should  be  gathered  from  all  parts.  Accordingly  it  is 
an  arrangement  of  nature  that  children  should  be  rest- 
less in  body  so  as  to  secure  an  all-round  physical  de- 
velopment, and  restless  in  spirit  in  order  that  they  may 
derive  materials  from  all  their  environment.  A  child 
may  have  a  more  or  less  strong  inherent  tendency  to 
develop  fixed  backgrounds,  but  at  early  stages  it  is 
unusual  to  find  this  tendency  very  prominent.  Our 
great  difficulty  is  the  instability  that  characterises 
the  youthful  background.  We  are  never  quite  sure 
that  the  ideas  of  this  minute  will  be  projected  against 
the  same  background  as  the  ideas  of  last.  Among 
grown-up  people  those  who  are  silly,  giggling,  flippant, 
are  usually  those  with  unstable  backgrounds.  What 
is  often  called  the  Associative  mind  is  of  this  class. 
No  doubt  the  force  of  association  tends  to  make  ideas 
cohere.  But  in  the  case  of  fluid  minds  association 


MENTAL  BACKGROUND  103 

exercises  its  power  rather  in  promoting  a  flow  of  ideas 
than  in  consolidating  ideas  into  organised  groups. 
A  word  is  enough  to  divert  the  stream  of  thought. 
Dame  Quickly  is  the  emeritus  example  of  a  mind  of  this 
sort  —  though,  unfortunately,  we  do  not  need  to  go 
30  far  afield  for  abundant  examples  of  the  type.  The 
background  against  which  the  ideas  of  Dame  Quickly 
project  themselves  can  hardly  be  called  stable.  It 
is  more  like  a  rapidly  moving  panorama  than  an  or- 
dinary picture. 

The  third  class  of  mind,  as  characterised  by  its  back- 
grounds, is  the  desirable  one  that  may  be  named  the 
plastic.  This  type  of  mind  forms  its  own  complexes 
with  fair  ease,  and  at  the  same  time  is  able  to  retain 
them  in  that  state  that  prevents  deliquescence  on  the 
one  hand  and  rigidity  on  the  other.  The  resulting 
backgrounds  are  mobile.  They  remain  steady  as  long 
as  they  are  required  to  be  steady,  but  are  ready  for 
immediate  change  if  that  is  found  desirable.  They  are 
stable  enough  to  allow  of  very  gradual  change,  and 
mobile  enough  to  submit  to  sudden  fluctuations  if  need 
be.  Nimble-witted  people  are  marked  by  a  high  degree 
of  mobility  of  background. 

To  illustrate  the  working  of  mental  backgrounds, 
take  the  cases  of  a  congregation  listening  to  a  sermon, 
students  listening  to  a  lecture,  and  a  person  reading  a 
poem.  In  the  sermon,  as  a  rule,  there  is  no  call  for  vio- 
lent change  of  background.  Frequently,  indeed,  the 
lines  are  laid  out  beforehand,  the  heads  are  given,  and 
the  work  of  the  preacher  is  to  develop  these  heads,  the 
work  of  the  listener  to  supply  the  appropriate  and  slowly 
changing  background.  So  with  the  instructive  lecture. 
Fact  after  fact  is  introduced,  but  for  each  fact  a  place 


104    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

has  been  prepared.  At  the  very  start  of  the  lecture 
the  teacher,  if  he  knows  his  business,  has  referred  to 
some  fact  that  he  is  sure  lies  within  the  knowledge  of 
his  hearers.  This  prepares  the  way  for  a  background 
different  from  that  which  previously  existed  in  the 
students'  minds.  As  a  rule  that  previous  background 
is  not  of  much  consequence.  It  is  usually  made  up  of 
floating  ideas  of  the  campus  or  stairs  or  notebooks  or 
whittling  pencils.  If  the  students  have  just  come  from 
an  examination,  or  from  a  college  row,  or  even  from 
a  specially  interesting  lecture,  the  power  of  the  back- 
ground they  bring  with  them  may  be  much  greater, 
and  much  more  difficult  for  the  new  lecturer  to  deal 
with.  Under  adverse  circumstances  like  these,  the 
teacher  has  two  courses  open  to  him.  He  may  begin 
with  a  particularly  striking  sentence,  in  the  hope  of 
causing  a  rapid  change  of  background,  in  which  case 
he  makes  an  assault  upon  the  attention  in  the  hope  of 
taking  it  by  storm.  Or  he  may  begin  by  saying  noth- 
ing to  which  he  attaches  much  importance  during  the 
first  five  minutes,  in  the  hope  that  the  old  background 
will  gradually  give  way,  and  enable  him  to  establish 
a  new  one  as  soon  as  he  begins  to  deal  with  the  real 
matter  of  his  lecture.  This  latter  method  is,  on  the 
whole,  more  likely  to  succeed.  Replacing  the  old  back- 
ground item  by  item  is  a  much  more  hopeful  proceed- 
ing than  an  attempt  to  wave  the  conjurer's  wand. 
A  background  cannot  be  called  up  at  will.  Recall 
is  not  quite  the  same  thing.  It  is  perhaps  not  very 
difficult  to  reinstate  the  background  of  a  previous 
lecture.  Indeed,  it  ought  to  be  easy,  for  all  the  help 
students  usually  get  is  the  dry  paragraph  that  follows 
the  colorless  opening:  "Gentlemen,  in_our  last  lecture 


MENTAL  BACKGROUND  105 

..."  But  a  real  beginning  is  different.  Why  is  it 
that  the  experienced  railway  reader  prefers  to  start  his 
journey  with  a  "begun"  novel?  And  if  it  is  a  little 
irksome  to  make  a  beginning  of  a  novel,  why  is  it  still 
harder  to  begin  to  read  a  play  ?  The  answer  is  clearly 
that  in  both  cases  there  is  no  background,  and  that  in 
the  case  of  the  play  the  background  is  more  remote 
than  in  the  novel,  where  the  author  at  least  does  his 
best  to  help  the  reader  in  supplying  a  background. 

In  reading  a  poem  we  are  often  called  upon  to  make 
rapid  and  violent  changes  of  background.  This  does 
not  mean  that  we  must  suddenly  change  the  whole 
body  of  thought  that  corresponds  to  James's  stream. 
In  reading  a  well-constructed  poem,  the  main  body  of 
thought  remains  constant  in  spite  of  the  rapid  changes 
called  for  by  the  accumulated  figures  of  speech.  The 
as  of  the  figure  suspends  the  main  interest  of  the  reader 
till  the  corresponding  so  releases  it  again.  At  Virgil's 
invitation 1  we  leave  the  two  Trojans  and  accompany 
him  to  the  teeming  bee-hive,  but  when  the  visit  is  over, 
we  gladly  return  to  ^Eneas  and  his  friend.  While  we 
are  with  the  bees,  what  has  become  of  the  Trojans  and 
the  Tyrians  ?  Has  the  background  of  country  life  dis- 
placed entirely  the  background  supplied  by  the  surging 
city?  Are  our  thoughts  with  the  bees  or  with  the 
Trojans  and  the  Tyrians?  Different  minds  act  dif- 
ferently here.  The  rigid  mind  prefers  to  remain  with 
the  Trojans  and  the  busy  city-builders:  it  resents  this 
interruption,  looks  at  the  bees  with  disapproval,  waits 
impatiently  till  the  poet  sees  fit  to  return  to  his  proper 
work.  The  fluid  mind,  on  the  other  hand,  accompanies 
the  poet  gladly,  forgets  all  about  the  Trojans,  and 

1  Mneid,  Book  I,  430. 


106    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

revels  in  the  new  scene.  The  man  of  plastic  mind  read- 
ily supplies  the  new  background  that  is  necessary,  but 
does  not  forget  the  old.  His  enjoyment  of  the  new 
background  is  affected  by  the  fact  that  it  has  a  relation 
to  the  old  one.  The  country  scene  has  a  different 
charm  for  him  here,  compared  with  what  it  would 
have  had  it  occurred,  say,  in  Wordsworth,  where  it 
would  appear  for  its  own  sake.  It  is  a  case  of  turbid 
media. 

Some  minds  treat  such  temporary  backgrounds  as 
ends  hi  themselves,  others  as  a  mere  part  of  a  wider 
whole.  Some  keep  the  Trojans  before  their  minds  all 
the  while  they  are  considering  the  bees.  The  interest 
for  minds  of  this  class  lies  mainly  in  the  relation  be- 
tween the  two  sets  of  ideas.  The  toiling  Tyrians  are 
set  over  against  the  busy  bees.  Other  minds  can  sus- 
pend, for  the  time  being,  the  background  of  Dido's 
new  city  without  letting  it  disappear  altogether.  The 
charm  of  comparison  comes  after  the  figure  has  been 
enjoyed  for  its  own  sake.  Yet  even  while  the  figure 
is  present  it  cannot  be  treated  quite  as  if  it  were  an 
independent  subject  of  thought.  It  lies  on  the  sur- 
face of  the  stream  of  thought,  it  is  true;  it  cannot  be 
denied  that  it  is  focal,  but  the  influence  of  the  whole 
undercurrent  of  the  stream  is  felt;  the  subconscious 
body  of  the  stream  influences  our  treatment  of  the 
surface  current. 

It  is  in  the  practical  affairs  of  life  that  there  is  a  call 
for  sudden  and  more  or  less  complete  changes  of  back- 
ground. The  different  business  calls  a  man  receives  in 
his  office  every  day  need  not  involve  a  greater  change 
of  background  than  we  have  seen  in  the  case  of  read- 
ing a  poem.  There  is  usually  sufficient  continuity  to 


MENTAL  BACKGROUND  107 

maintain  the  connection  between  the  parts.  But  if  a 
man  is  interrupted  in  his  business  by  household  cares, 
or  by,  say,  church  concerns,  the  difficulty  of  main- 
taining a  stable  background  is  greatly  increased.  A 
man  called  away  suddenly,  after  a  hard  bargain  with 
a  business  rival,  to  deal  with  a  case  of  conscience  can 
hardly  make  the  necessary  change  of  background  with 
the  required  rapidity.  In  this  case  there  has  to  be  a 
complete  change  in  the  body  of  the  stream  of  conscious- 
ness before  the  required  background  can  be  attained. 
What  happens  as  a  matter  of  fact  is  that  at  the  beginning 
of  the  new  interview  there  is  a  good  deal  of  confusion  of 
thought.  The  new  background  is  not  distinct.  It  is 
affected  according  to  the  laws  of  turbid  media  by  the 
background  that  has  not  yet  had  time  to  disappear. 
After  a  little,  thought  becomes  clearer,  ideas  are  grad- 
ually rearranged,  the  old  background  becomes  so  dun 
as  not  to  interfere  with  the  new,  and  the  change  is 
effected. 

So  far  we  have  been  dealing  with  backgrounds  as 
wholes.  But  the  elements  that  make  up  a  given  back- 
ground are  not  combined  as  simple  and  independent 
units.  They  are  all  grouped  together  more  or  less 
firmly  into  different  complexes,  and  these  complexes 
form  the  real  units  of  combination.  In  all  descriptive 
writing  and  speaking  it  is  assumed  that  the  reader  or 
hearer  has  the  necessary  complexes  at  hand  ready-made. 
The  more  cultured  the  audience  with  reference  to  a  par- 
ticular subject  the  greater  the  degree  of  complexity  the 
expositor  is  entitled  to  assume  in  the  combination  unit. 
When  a  novelist  sets  his  scene  in  a  mediaeval  castle,  he 
assumes  that  his  readers  have  a  complex  of  ideas  that 
corresponds  to  his  own.  He  does  not  begin  with  the 


108    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

elementary  ideas  of  portcullis,  barbican,  moat,  draw- 
bridge, keep,  bailey;  he  assumes  these  to  be  present 
and  arranged  in  a  particular  way.  If  the  novelist  uses 
the  words  "Norman  castle/'  he  assumes  what  he  has 
assumed  before,  but  limits  the  possible  combinations 
of  the  elements.  If  he  mentions  the  century  in  which 
the  castle  was  built,  he  makes  a  still  higher  demand 
on  his  readers'  ability  to  conform  to  standard  in  form- 
ing complexes.  If  the  novelist  thereafter  feels  called 
upon  to  expand  into  description,  he  concerns  himself 
entirely  with  those  parts  of  the  castle  in  question  that 
are  more  or  less  peculiar  to  it.  As  a  matter  of  fact, 
we  have  all  a  large  supply  of  ready-made  complexes 
that  are  in  themselves  invariable  and  may  be  used  as 
composite  units  to  build  up  any  desired  whole.  The 
skill  of  the  poet,  the  teacher,  and  the  novelist  is  shown 
in  the  way  they  manipulate  these  complexes  to  form 
the  whole  that  suits  their  immediate  purpose. 
-  The  first  general  remark  to  be  made  about  these 
ready-made  complexes  is  that  they  owe  some  of  their 
characteristics  to  the  preferred  sense  of  the  person  in 
whose  mind  they  are  formed.  It  is  well  known  that 
minds  differ  in  the  class  of  impressions  that  affect  them 
most.  There  are  those  who  depend  mainly  upon  the 
eye.  These  are  termed  visuals.1  For  them  every- 
thing that  is  comfortably  assimilated  by  the  mind  has 
been  treated  in  terms  of  form,  size,  and  colour.  Audiles, 
on  the  other  hand,  prefer  to  deal  with  sounds.  An 
audile  enjoys  being  read  to;  a  visual  is  unhappy  unless 
he  can  read  for  himself.  At  the  play  the  visual  is  most 
impressed  by  the  scenery,  the  dresses,  the  gestures; 
the  audile  by  the  dialogue,  the  songs,  the  music.  Those 

1  Some  writers  prefer  the  term  visiles. 


MENTAL  BACKGROUND  109 

that  are  known  as  tactiles  reduce  everything  as  far  as 
possible  to  impressions  of  the  sense  of  touch.  When 
we  speak  of  a  cat,  the  visual  has  an  impression  of  its  size, 
form,  and  colour;  the  audile  remembers  its  purring  or 
its  caterwauling;  the  tactile  reproduces  in  his  conscious- 
ness the  pleasant  feel  of  its  fur.  The  senses  of  smell 
and  taste  are  not  usually  included  in  this  classification: 
we  do  not,  as  a  rule,  speak  of  gustatives  or  olfactives. 
This  is  probably  because  these  senses  are  of  inferior 
importance  in  the  building  up  of  knowledge.  There  is 
no  doubt,  however,  that  they  also  have  a  considerable 
effect  in  modifying  the  way  in  which  different  people 
regard  the  same  thing.  A  caution  is  here  not  out  of 
place.  We  must  not  make  the  distinction  too  promi- 
nent. It  is  not  to  be  supposed  that  an  audile  gets  most 
of  his  information  through  the  ear,  but  only  that  that 
is  the  best  way  to  get  at  that  particular  person.  He 
prefers  to  have  his  knowledge  come  through  the  ear. 
It  is  quite  possible  that  the  psycho-physicists  may  by 
and  by  be  able  to  arrange  the  senses  in  their  precise 
order  of  merit  as  knowledge-providers.  But  even  if 
this  absolute  order  of  merit  were  to  be  published  to- 
morrow, it  would  in  no  way  affect  the  fact  that  people 
have  their  preferred  sense.  An  audile  may  learn  abso- 
lutely more  from  the  sense  of  sight  than  from  the  sense 
of  hearing,  and  be  an  audile  none  the  less. 

In  dealing  with  mental  backgrounds  most  of  us  have 
the  prevailing  impression  of  sight.  For  this  there  are 
obvious  reasons.  There  are  more  visuals  than  audiles 
in  the  world;  and  in  addition,  the  very  word  back- 
ground drives  us  by  association  to  visual  impressions. 
Moreover,  for  the  purpose  of  school,  visual  back- 
grounds are  more  useful  than  any  others,  for  the  very 


110    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

sufficient  reason  that  we  can,  to  some  extent  at  least, 
compare  them  with  each  other  through  the  intermediary 
of  an  external  standard.  If  the  pupil  is  asked  to  think 
of  a  country  town,  a  picture  at  once  rises  in  his  mind. 
This  is  his  picture  of  a  country  town.  If  it  is  analysed, 
it  will  be  found  in  all  probability  that  it  owes  most  of 
its  characteristics  to  one  particular  town  with  which  he 
is  familiar,  or  in  connection  with  which  he  made  his 
first  acquaintance  with  country  towns.  Further,  the 
fewer  country  towns  the  pupil  has  seen  the  clearer  is 
the  picture  that  rises  in  his  mind.  To  one  who  has  seen 
a  great  number  of  such  towns  there  is  a  vagueness  about 
the  picture.  The  peculiarities  of  the  different  towns 
are  contrary  ideas,  and  therefore  arrest  each  other. 
Accordingly  there  is  a  struggle  going  on  all  along  the 
line,  and  only  the  absolutely  common  elements  remain 
clear.  If,  now,  the  man  of  many  country  towns  is 
determined  to  have  a  clear  picture,  he  can  usually  suc- 
ceed; but  the  price  that  he  pays  is  the  loss  of  the  pic- 
ture of  a  country  town  in  general,  and  the  adoption 
of  a  particular  town.  His  town  is  the  pictured  image 
of  what  he  has  actually  seen.  Indeed  this  is  the  most 
common  form.  Instead  of  having  a  vague  background 
ready-made,  most  people  have  more  or  less  vague  mem- 
ories of  backgrounds  that  actually  exist.  At  first  sight 
it  may  seem  that  there  is  no  harm  in  this,  and  some 
may  even  be  prepared  to  say  that  these  pictures  are 
better  than  vague  generalised  outlines.  But  when 
it  comes  to  supplying  backgrounds  to  ideas  presented 
by  another,  it  will  be  found  that  misunderstandings 
are  apt  to  arise  from  the  detailed  character  of  the  pic- 
ture. The  teacher's  exposition  may  not  fit  into  the 
pupil's  picture  because  some  detail  in  that  picture  is 


MENTAL  BACKGROUND  111 

inconsistent  with  something  the  teacher  has  said.  This 
detail  is  not  essential  to  the  general  background  de- 
manded by  the  teacher,  and  should  therefore  be  elim- 
inated. In  a  description,  for  example,  the  teacher 
may  speak  of  the  church  as  being  on  the  north  of  the 
market-place,  while  in  the  pupil's  picture  it  is  on  the 
east.  The  pupil's  mind  resents  this,  and  a  wrong  atti- 
tude results.  With  a  purely  generalised  picture  of  the 
village  the  church  can  be  put  anywhere  without  rous- 
ing opposition. 

A  very  interesting  as  well  as  useful  exercise  is  to  take 
the  catalogue  of  an  art  exhibition  before  seeing  the 
pictures,  and  try  to  realise  what  sort  of  picture  corre- 
sponds to  each  of  the  descriptive  titles.  The  man  of 
many  galleries  succeeds  fairly  well.  His  mental  picture 
of  even  such  a  tantalising  description  as  "Portrait  of 
a  Lady"  is  not  usually  far  wrong.  But  to  the  ordinary 
lay  mind  there  will  be  little  but  disappointment. 
"Chill  October,"  "With  Daisies  Pied,"  "In  Spate," 
"Where  the  Bee  Lurks,"  "Boors  Drinking,"  "The 
Village  Wedding,"  all  raise  pictures  in  our  minds  that 
do  not  correspond  to  what  we  find  in  the  frames. 
Yet  we  cannot  blame  the  painters:  in  each  case  we 
are  constrained  to  admit  that  the  picture  justifies  the 
name,  and  in  most  cases  we  are  prepared  to  acknow- 
ledge that  the  painter's  idea  is  better  than  ours.  But 
for  all  that,  the  two  pictures,  his  and  ours,  are  not 
the  same.  So  with  description.  However  carefully  a 
town  may  be  described  to  you, — in  words, — you  will 
always  find  that  when  you  reach  the  town  itself  it  is 
not  quite  what  you  had  pictured  it  to  be.  You  cannot 
accuse  your  friend  of  describing  it  falsely  or  carelessly. 
Everything  he  has  told  you  is  justified  by  what  you  see. 


112    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

You  admit  that  it  is  exactly  as  he  described  it  to  you  — 
only  it  is  different. 

Now  if  practical  issues  depend  upon  this  description, 
how  easily  you  might  be  misled.  Your  picture  corre- 
sponds at  all  the  points  of  contact  with  the  description, 
but  at  all  other  points  your  picture  is  independent  of 
the  reality,  and  has  no  guidance.  Let  us  not  forget 
that  the  very  vagueness  of  our  backgrounds  may  have 
its  use.  It  is  this  quality  that  enables  us  to  fit  them 
into  so  many  different  frames.  If  any  discrepancy 
arises,  it  can  be  readily  remedied,  while  as  for  the  remain- 
ing unexpressed  details  they  do  not  matter,  so  long  as 
they  do  not  imply  a  hidden  contradiction.  We  some- 
times forget  how  much  work  the  reader  or  hearer  has 
to  do  as  the  apparently  passive  partner  in  the  process 
of  Exposition.  The  writer  no  doubt  brings  his  ideas 
together  and  lays  them  before  us  with  more  or  less  skill  ; 
but  the  reader  has  to  supply  his  own  backgrounds,  and 
see  that  they  agree  with  the  ideas  projected  against 
them.  Sometimes  it  happens  that  a  discrepancy 
arises  because  in  the  mind  of  the  writer  the  idea  was 
originally  projected  against  a  false  background,  and 
the  error  is  detected  against  the  more  accurate  back- 
ground supplied  by  the  reader.1  More  frequently  the 
reader's  faulty  background  is  exposed  by  the  process 
of  projecting  the  writer's  ideas  against  it.  A  schoolboy 
who  had  never  been  in  Edinburgh  objected  to  his  lesson 
book  for  describing  an  attempt  on  Edinburgh  Castle 
made  from  the  steep  cliff  on  the  west  side.  His  argu- 
ment was  that  the  steep  cliff  was  on  the  east  side. 
When  asked  to  justify  his  criticism,  he  had  nothing  to 
say  but  a  reiteration  that  the  account  must  be  wrong; 

1  This  is  worked  out  in  greater  detail  in  Chap.  XIV,  p.  344. 


MENTAL  BACKGROUND  113 

this  seemed  to  him  self-evident.  It  was  only  when 
hard  pressed  by  his  teacher,  who  pointed  out  that  the 
access  was  quite  easy  from  the  east,  that  the  boy  scorn- 
fully explained  that  climbing  a  high  cliff  out  of  small 
boats  was  not  what  he  considered  an  easy  approach. 
The  mention  of  boats  led  to  further  enquiries,  when 
it  came  out  that  the  boy  was  dealing  with  the  only 
castle  he  had  seen,  which  happened  to  be  Dunnottar 
Castle  in  the  northeast  of  Scotland,  where  certainly 
his  objection  held.  He  had  simply  taken  the  word 
castle  to  connote  all  the  elements  of  the  single  castle 
he  had  seen. 

Apart  from  the  errors  arising  from  different  concep- 
tions of  the  content  of  the  mental  backgrounds,  there  is 
another  source  of  danger.  Exposition  may  fail  because 
of  what  may  be  called  mental  parallax.  The  teacher 
and  the  pupil  may  project  the  same  ideas  against  identi- 
cal backgrounds  and  yet  come  to  different  conclusions, 
because  they  view  the  ideas  from  different  standpoints. 
The  teacher  may  project  a  given  idea  against  one  part 
of  the  background,  and  the  pupil  against  another. 
Much  depends  upon  the  point  of  view.  Nothing  is 
more  important  in  Exposition  than  the  selection  of  the 
proper  point  of  view  and  the  securing  of  the  coincidence 
of  the  pupil's  standpoint  with  the  teacher's. 

The  danger  of  a  wrong  point  of  view  may  be  illus- 
trated from  our  own  adult  experience  when  reading 
novels.  Sometimes  the  author  takes  it  upon  him  to 
keep  us  for  several  chapters  in  the  company  of  the  vil- 
lain and  his  accomplices.  Gradually  we  begin  uncon- 
sciously to  look  at  things  from  the  villain's  standpoint. 
There  is,  of  course,  in  this  case  no  real  harm  done;  it 
is  only  a  matter  of  tone.  But  the  effect  is  quite  per- 


114    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

ceptible.  By  and  by,  when  some  virtuous  person  in 
the  story  comes  along  and  interferes  with  the  villain's 
plans,  we  experience  a  distinct,  if  momentary,  an- 
noyance.1 

It  must  not  be  supposed  that  the  point  of  view  is 
limited  in  its  effects  to  the  tone  value  of  a  lesson.  It 
is  equally  important  in  Exposition  that  deals  with  the 
cognitive  side.  In  the  more  practical  parts  of  our 
teaching,  in  which  imitation  is  largely  relied  upon,  we 
find  the  point  of  view  of  the  first  importance.  In  the 
various  exercises  in  which  the  teacher  shows  the  pupils 
by  example  exactly  what  they  are  to  do,  there  is  a 
special  form  of  confusion  that  arises  from  difference 
in  the  point  of  view.  This  is  the  distinction  between 
right  and  left.  In  ordinary  life  it  is  common  to  find  a 
certain  amount  of  confusion  between  the  right  and 
the  left.  Every  stranger  who  asks  his  way  in  a  great 
city  has  abundant  evidence  of  the  existence  of  this  con- 
fusion. It  is  always  well  to  test  each  direction  at  every 
turning.  For  "third  turning  to  the  right"  we  have 
frequently  to  read  "third  turning  to  the  left."  This 
arises  partly  from  the  confusion  that  inevitably  occurs 
in  an  appreciable  percentage  of  cases  when  we  are 
dealing  with  two  opposed  directions.  We  have  the 
same  confusion  to  a  less  degree  between  east  and  west 
on  a  map,  but  not  nearly  so  frequently  between  north 
and  south.  There  may  be  other  causes  for  the  differ- 
ence, but  there  can  be  little  doubt  that  east  and  west 
are  more  readily  confused  because  of  their  connection 
with  the  right  and  left  of  the  map. 

The  fact  that  the  wayfarer  and  the  policeman  who  is 
directing  him  usually  stand  facing  each  other  may  have 

1  For  further  illustration,  see  Chap.  X. 


MENTAL  BACKGROUND  115 

something  to  do  with  the  resulting  confusion.  The 
wayfarer's  left  is  the  policeman's  right.  This  source 
of  error  is  not  absent  from  school.  The  drill-master 
and  the  sewing  mistress  standing  in  front  of  their  class 
and  trying  to  illustrate  some  motion  run  serious  risk 
of  confusion.  They  sometimes  meet  the  difficulty  by 
facing  the  same  way  as  the  class,  and  doing  the  best 
they  can  under  the  circumstances.  The  position  is 
awkward  for  both  pupils  and  teacher,  but  is  found  to 
be,  on  the  whole,  the  best  way  out  of  an  almost  impossible 
situation.  An  alternative  is  to  stand  facing  the  class, 
and  then  give  the  demonstration  with  reversed  arms; 
that  is,  the  teacher  uses  the  right  arm  when  he  wishes 
the  pupil  to  use  the  left,  and  vice  versa.  This  naturally 
requires  special  training  on  the  part  of  the  teacher. 


CHAPTER  V 
SUGGESTION  IN  EXPOSITION 

WE  have  seen  that  the  process  of  influencing  another 
mind  acquires  all  the  interest  of  a  mystery,  and  the 
wonder  of  our  being  able  to  act  upon  the  mind  of  an- 
other at  all  is  increased  when  we  discover  that  our  own 
minds  are  far  from  being  entirely  at  our  own  disposal. 
Psychologists  are  fond  of  pointing  out  that  we  cannot 
call  up  ideas  at  will; 1  that  we  are  more  or  less  at  the 
mercy  of  chance  recall; 2  that  if  "activity  seems  to  be 
self-caused  change,"  3  then  we  have  no  such  thing  as 
mental  activity; 4  that  even  the  inventor  has  to  wait  for 

1  "Volition  has  no  power  of  calling  up  images,  but  only  of  rejecting 
and  selecting  from  those  offered  by  spontaneous  redintegration.  But 
the  rapidity  with  which  the  selection  is  made,  owing  to  the  familiar- 
ity of  the  ways  in  which  spontaneous  redintegration  runs,  gives  the 
process  of  reasoning  the  appearance  of  evoking  images  that  are  fore- 
seen to  be  conformable  to  the  purpose.  There  is  no  seeing  them  be- 
fore they  are  offered;  there  is  no  summoning  them  before  they  are 
seen."— Shadworth  H.  Hodgson :  The  Theory  of  Practice,  Vol.  I,  p.  400. 

3  See  the  whole  of  the  section  on  "Command  of  the  Thoughts"  in 
Professor  Alexander  Bain's  The  Emotions  and  the  Will,  pp.  369-382, 
particularly  the  famous  passage  (pp.  376-377)  in  which  the  mind  is 
compared  to  a  wild  beast  waiting  to  spring  upon  its  prey,  as  soon 
as  it  appears,  but  quite  unable  to  hasten  that  appearance. 

*  F.  H.  Bradley:   Appearance  and  Reality,  p.  64. 

*  G.  F.  Stout :  Analytical  Psychology,  Vol.  I,  p.  155 :  "  It  seems  clear 
that  if  our  whole  conscious  existence  is  so  constantly  and  thoroughly 
dependent  on  factors  extraneous  to  it,  there  is  no  room  anywhere 
within  it  for  purely  immanent  causality.     It  is  impossible  to  find  any 
bit  of  mental  process  which  is  determined  purely  from  within." 

116 


SUGGESTION  IN  EXPOSITION  117 

some  outside  spark  to  touch  off  his  loaded  intelligence.1 
If  we  are  distrustful  of  the  evidence  of  the  professional 
psychologists,  we  may  turn  to  the  evidence  of  the  intel- 
ligent layman.  The  following  is  the  view  of  a  writer, 
not  a  professional  philosopher,  whose  name  is  a  house- 
hold word  on  both  sides  of  the  Atlantic.  The  passage 
occurs  in  a  private  letter  to  the  author:  — 

"A  curious  thing  is  the  mind,  certainly.  It  originates  nothing, 
creates  nothing,  gathers  all  its  materials  from  the  outside,  and 
weaves  them  into  combinations  automatically,  and  without  any- 
body's help  —  and  doesn't  even  invent  the  combinations  itself, 
but  draws  the  scheme  from  outside  suggestion.  .  .  . 

"  It  does  seem  a  little  pathetic  to  reflect  that  man's  proudest  pos- 
session —  his  mind  —  is  a  mere  machine ;  an  automatic  machine ; 
a  machine  which  is  so  wholly  independent  of  him  that  it  will  not 
take  even  a  suggestion  from  him,  let  alone  a  command,  unless  it  suits 
its  humour ;  that  both  command  and  suggestion,  when  offered,  origi- 
nate, not  on  the  premises,  but  must  in  all  cases  come  from  the  outside ; 
that  we  can't  make  it  stick  to  a  subject  (a  sermon,  for  instance)  if 
an  outside  suggestion  of  sharper  interest  moves  it  to  desert ;  that 
our  pride  in  it  must  limit  itself  to  ownership,  ownership  of  a 
machine  —  a  machine  of  which  we  are  not  a  part,  and  over  whose 
performances  we  have  nothing  that  even  resembles  control  or  au- 
thority. It  is  very  offensive.  Any  tramp  that  comes  along  may 
succeed  in  setting  it  in  motion,  but  you  can't.  If  you  say  to  it : 
'  Examine  this  solar  system,  or  this  Darwinian  Theory,  or  this  potato,' 
you  can  only  say  it  or  think  it  when  the  inspiration  has  come  to  you 
from  outside.  And  to  think  that  Shakespeare  and  Watt,  and  we 

1  F.  Paulhan :  Psychologic  de  I' Invention,  p.  10.  Taking  Newton  as 
a  typical  case,  Paulhan  deals  with  the  two  essential  elements,  (1)  the 
total  results  of  Newton's  previous  thinking,  and  (2)  the  fall  of  the  apple 
(or  its  equivalent)  as  the  immediate  cause  of  the  discovery:  "L'un 
indique  la  preparation  lente  de  1'invention,  la  tendance  qui  travaille 
a  se  completer,  1'idee  confuse  cherchant  1'ele'ment  qui  la  pr6cisera; 
1'autre  signale  1'occasion  venue,  Tenement  nouveau  qui  se  pr£sente 
engage  dans  la  perception  (ou  dans  1'idee)  d'ou  1'esprit  saura  1'ab- 
straire,  et  determine  la  synthese  nouvelle.  la  creation  intellectuelle." 


118    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

others  can't  even  combine  our  idea-catches  on  plans  original  with 
ourselves,  but  that  even  the  combination-scheme  must  come  from 
the  outside  —  gathered  from  reading  and  experience. 

"  Meantime,  which  is  I  and  which  is  my  mind  t  are  we  two  or  are  we 
one  ?  However,  it  is  not  important,  for  if  we  say,  '  I  will  think, ' 
neither  I  nor  the  mind  originated  the  suggestion  —  it  came  from 
outside." 

All  this  may  be  very  depressing  and  even  "offensive" 
to  the  ordinary  man.  To  the  teacher  it  is  full  of  en- 
couragement. For  it  must  be  remembered  that  in  the 
process  described  he  plays  the  part  of  the  tramp.  He 
does  the  stimulation  from  the  outside.  Archimedes 
prayed  for  a  fulcrum  for  his  lever,  and  promised  that 
if  his  prayer  were  answered  he  would  move  the  world. 
But  as  he  could  not  step  off  the  earth,  the  TTOV  o-rw  he 
desired  remained  an  aspiration.  The  prayer  that  was 
refused  to  Archimedes  hi  the  physical  world  has  hi 
the  mental  been  granted  to  the  humblest  teacher.  So 
far  from  complaining  that  we  are  "prisoned  in  sepa- 
rate consciousness"  and  cannot  share  the  consciousness 
of  our  pupils,  we  ought  to  rejoice  that  we  are  enabled  to 
stand  outside  the  mind-world  of  our  pupils,  and  from 
our  vantage  ground  there  move  that  world.  To  what 
extent  we  can  move  it  is  a  different  question.  For 
here  we  come  to  an  aspect  of  the  matter  that  restores 
our  self-respect  as  human  beings,  though  it  diminishes 
our  power  as  teachers.  The  writer  just  quoted  is  un- 
duly depressed.  It  is  true  that  the  tramp  can  for  the 
moment  direct  our  attention  this  way  or  that  at  his 
will  and  against  ours.  But  the  amount  of  attention 
we  give  depends  not  on  the  tramp,  but  on  the  nature 
and  content  of  the  mind  he  seeks  to  manipulate.  The 
power  of  the  teacher,  like  the  power  of  the  tramp,  is 


SUGGESTION  IN  EXPOSITION  119 

limited  to  directing  the  mind's  attention.  The  deter- 
mination of  the  amount  and  the  duration  of  the  at- 
tention lies  with  the  mind  attacked. 

For  the  comfort  of  the  teacher,  and  the  discourage- 
ment of  the  tramp,  it  is  well  to  remember  that  the  time 
element  is  very  important  to  the  full  understanding  of 
this  matter.  The  ordinary  tramp  can  command  im- 
mediate but  only  momentary  attention  to  a  particular 
topic.  If  he  happens  to  know  the  sort  of  things  we  are 
interested  in,  and  is  able  to  talk  intelligently  about 
them,  he  no  doubt  is  in  a  position  to  retain  our  atten- 
tion for  quite  a  long  while.  But  in  doing  so  he  ceases 
to  form  a  part  of  mere  external  nature.  He  is  no  longer 
a  mere  tramp  acting  at  haphazard.  He  is  acting 
deliberately,  and  with  a  knowledge  of  what  he  is  about. 
He  is  really  usurping  the  teacher's  place.  Nor  can  we 
reasonably  resent  the  exercise  of  the  power  he  has  over 
our  minds.  After  all,  it  is  we  who  have  put  this  power 
into  his  hands.  It  is  because  we  are  what  we  are  that 
he  is  able  to  manipulate  us.  To  a  certain  extent  he  can 
make  us  act  according  to  his  will,  but  he  can  do  this 
only  by  obeying  the  laws  of  our  nature,  by  appealing 
to  what  he  knows  to  be  in  us.  He  must  adapt  himself 
to  us.  He  must  respect  our  individuality.  He  must 
stoop  to  conquer. 

Having  learnt  the  lesson  of  the  tramp,  it  is  now  our 
business  to  discover  what  means  we  have  at  our  dis- 
posal to  manipulate  effectively  the  mental  content  of 
another  mind.  Immediate  recall  in  which  an  idea 
forces  its  way  into  consciousness  by  the  mere  strength 
of  its  accumulated  presentative  activity  offers  no 
difficulty,  and  mediate  recall  that  takes  the  form  of 
sense  stimulation,  as  in  the  case  of  sights,  smells,  and 


120    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

sounds  reestablishing  a  whole  that  formerly  existed, 
is  almost  equally  free  from  trouble.  But  in  the  ordi- 
nary case  in  which  one  idea  recalls  a  whole  mass  we 
have  a  notable  complication.  For  an  idea  usually 
belongs  to  several  groups.  Certain  ideas,  it  is  true, 
are  for  most  minds  restricted  to  one  definite  mass. 
They  have  nothing  whatever  to  do  with  any  other  mass. 
It  is  the  function  of  technical  terms  to  limit  such  ideas 
to  their  proper  mass,  and  thus  prevent  confusion.  The 
word  ohm  is,  I  believe,  restricted  to  the  science  of  elec- 
tricity, and  for  the  ordinary  person  has  no  connection 
with  any  other  group  of  ideas.  Even  here,  however, 
I  have  no  doubt  that  in  the  mind  of  a  competent  elec- 
trician the  idea  of  ohm  will  have  connections  with  sev- 
eral masses.1 

Speaking  generally,  every  idea  forms  a  part  of  several 
masses.  When  an  idea,  then,  obtains  admission  into  the 
field  of  consciousness  and  proceeds  to  introduce  others 
by  mediate  recall,  the  question  arises:  Of  the  various 
masses  with  which  it  is  connected,  which  will  it  favour, 
which  will  it  tend  to  reinstate  ? 

At  first  sight  the  obvious  answer  is  the  strongest 
mass;  that  is,  the  mass  that  is  richest  in  elements,  is 
best  arranged,  and  has  the  greatest  accumulated  pre- 
sentative  activity.  Reflection  shows  that  if  this  were 
so,  then  in  a  given  mind  at  a  given  stage  the  same  idea 
must  always  call  up  the  same  mass.  But  experience 
proves  that  this  is  not  the  case.  It  has  to  be  observed 

1  On  making  a  testing,  casual  reference  to  the  term  in  conversation 
with  a  distinguished  physicist,  Dr.  William  Garnett,  Educational 
Adviser  to  the  London  County  Council,  I  found  that  in  his  mind  it 
formed  part  of  an  historical  mass,  an  economic  mass,  an  educational 
mass,  a  laboratory  mass,  a  workshop  mass,  a  literary  mass  —  at  this 
point  we  were  interrupted. 


SUGGESTION   IN  EXPOSITION  121 

that  we  are  not  here  dealing  with  the  effect  of  the  same 
idea  on  different  minds.  It  is  easy  to  guess  the  mass 
that  a  given  idea  will  recall  in  the  case  of  chosen  types 
of  men.  The  idea  of  vine  will  naturally  recall  his  green- 
house to  the  retired  merchant  who  is  fond  of  garden- 
ing, to  the  bon  vivant  his  favourite  wine,  to  the  devotee 
the  fifth  chapter  of  St.  John,  to  the  man  home  from 
Europe  the  slopes  of  the  Rhine  or  of  Burgundy,  to  the 
art-lover  certain  pictures  and  schools  of  painting,  to 
the  botanist  some  particularly  long  words.  All  this  is 
plain  sailing.  But  suppose  we  take  the  case  of  a  man 
who  combines  the  six  conditions.  It  is  surely  not  im- 
possible to  find  an  old  gentleman  eager  about  his  green- 
houses, fond  of  wines  and  pictures,  an  enthusiastic 
amateur  hi  botany,  full  of  memories  of  happy  walking 
tours  on  the  continent,  and  withal  a  constant  church- 
goer and  Bible-reader.  He  would  be  a  rash  man  who, 
without  knowing  the  old  gentleman,  would  venture  to 
predict  which  of  the  six  masses  the  idea  of  vine  would 
call  up.  Even  if  we  made  his  acquaintance  and  dis- 
covered which  masses  had  the  greatest  power  in  his 
consciousness,  we  would  have  only  a  slight  probability 
in  our  favour  in  guessing  the  strongest  mass  as  the  one 
to  be  recalled.  On  the  other  hand,  if  we  learn  that  the 
idea  was  brought  before  him  while  walking  in  his  garden 
on  an  autumn  evening  when  he  had  just  become  aware 
of  the  first  appearance  of  frost  for  the  year,  we  may 
with  more  confidence  foretell  the  direction  of  his  ideas. 
Yet  even  under  these  circumstances,  if  the  old  gentle- 
man had  during  the  afternoon  given  instructions  about 
heating  the  greenhouses,  and  so  had  his  mind  easy  on 
the  practical  side,  and  if  the  friend  with  whom  he  was 
walking  in  the  garden  had  been  recalling  escapades 


122    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

during  their  old  Burgundy  tramp,  the  chances  are  that 
the  idea  of  vine  would  rouse  the  geographical  and 
reminiscent  mass. 

Before  we  can  foretell  the  course  of  recall,  we  must 
know  (1)  the  contents  of  the  mind  in  question  and 
the  relative  accumulated  presentative  activities  of  the 
masses;  (2)  the  conditions  under  which  the  mediating 
idea  is  presented;  (3)  the  actual  contents  of  the  con- 
sciousness immediately  preceding  the  presentation. 

It  is  obvious  that  this  is  no  mere  theoretical  problem. 
We  are  here  dealing  with  the  fundamental  problem  of 
Exposition.  We  desire  a  given  mind  to  act  in  a  given 
way.  Our  first  step  must  be  to  learn  the  laws  accord- 
ing to  which  it  acts,  and  the  conditions  under  which 
these  operate.  Having  acquired  this  knowledge,  we 
are  able  to  interfere  effectively  with  the  course  of 
thought  in  the  mind  of  another.  In  ordinary  life  we 
are  continually  doing  this,  often  quite  unconsciously. 
Our  every  action  in  relation  to  others  cannot  but  modify 
the  course  of  thought  in  those  others.  Our  very  pres- 
ence often  accomplishes  such  a  modification  without 
our  even  being  aware  of  the  existence  of  the  person 
upon  wliose  mind  we  have  exercised  an  influence.  For 
we  have  seen  that  we  are  all  to  a  great  extent  at  the 
mercy  of  external  suggestion. 

In  applying  suggestion  for  our  special  purposes,  then, 
the  first  consideration  in  presenting  a  new  idea  is 
to  discover  against  which  background  it  is  likely  to 
be  projected.  Apart  from  any  special  circumstances 
that  may  complicate  individual  cases,  there  are  certain 
backgrounds  that  may  be  called  the  normals  for  cer- 
tain ideas.  If  this  mark  1 3  be  placed  upon  a  black- 
board, we  are  entitled  to  assume  that  it  will  be  projected 


SUGGESTION  IN  EXPOSITION  123 

against  a  background  of  numerals  and  read  as  thirteen. 
But  if  we  place  the  word  Ethel  before  it  and  the  word 
Jones  after  it,  we  may  be  certain  that  it  will  be  thrown 
against  a  literal  background,  and  read  as  the  initial 
of  one  of  the  names  of  a  person.  In  nearly  every  case 
there  is  a  preferential  background  against  which  an 
isolated  idea  will  be  normally  projected.  Naturally 
this  varies  according  to  the  content  of  the  individual 
mind.  But  examination  will  show  that  there  is  a  gen- 
eral as  well  as  a  personal  preferential  background  for 
each  idea.  It  is  useful  for  teachers  to  look  into  these 
preferences  both  personal  and  general. 

Take  the  case  of  homonyms.  If  the  word  one  is 
uttered,  most  people  who  hear  it  will  project  it  against 
a  numerical  background,  though  some  will  connect  it 
with  win.  So  with  the  word  two :  the  numerical  back- 
ground prevails,  though  in  this  case  there  are  three 
homonyms  to  choose  among.  It  is  clear  that  it  is  not 
mere  familiarity  with  the  word  that  determines  the 
choice  here,  for  to  occurs  more  frequently  in  ordinary 
reading  and  writing  than  does  two.  Speaking  generally, 
a  substantive  meaning  has  the  preference  over  a  tran- 
sitive l  meaning.  I  should  have  been  inclined  to  make 
the  statement  without  the  reservation,  had  it  not  been 
for  the  results  of  certain  experiments  that  I  made  to 
verify  my  general  impression,  which  was  based  on 
ordinary  observation.  I  selected  five  homonyms 
and  pronounced  the  sounds 2  to  various  classes  of  pupils 
who  were  instructed  to  write  down  without  hesitation 
the  word  that  occurred  to  them.  I  have  classified  the 

1  See  p.  43. 

2  The  invariable  sequence  of  the  sounds,  as  dictated,  was :  one,  be, 
rain,  by,  to. 


124     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 


results  into  three  groups.  Group  I  (representing  the 
work  of  about  600  pupils)  includes  only  pupils  between 
9  and  10;  Group  II  (about  2500  pupils)  represents 
the  work  of  pupils  of  ages  varying  from  11  to  15, 
the  ages  being  pretty  evenly  distributed;  Group  III 
(close  on  500  persons)  gives  the  reactions  of  under- 
graduate students  of  ages  ranging  from  19  to  22:  — 


HOMONYMS 

GROUP  I 

GROUP  II 

GROUP  III 

Percentage 

Percentage 

Percentage 

One     

99.1 

96.3 

92.7 

Won   

.9 

3.7 

7.3 

Be       

96.6 

73.6 

47.1 

Bee     

3.4 

26.4 

40.0 

Borb1    .     .     .     . 

12.9 

Rain   

99.4 

76.8 

86.0 

Reign       .... 
Rein    

.6 

22.1 
1.1 

11.2 
2.8 

By 

96.6 

690 

52.7 

Buy 

1.7 

25.1 

38.1 

Bye 

1.7 

5.9 

9.2 

Two    .     .          .     . 

3  7 

43  4 

77.2 

To  

92.6 

43.4 

12.6 

Too     

3.7 

13  2 

102 

Practical  teachers  will  have  little  difficulty  in  ac- 
counting for  the  differences  in  the  various  groups. 
The  little  children  took  the  point  of  view  of  the  dicta- 
tion lesson,  and  if  they  did  happen  to  know  any  other 
form  than  the  obvious  one,  preferred  to  stick  to  what 

1  Groups  I  and  II  had  been  warned  that  words  were  expected; 
this  accounts  for  the  absence  of  the  mere  letters  in  their  case. 


SUGGESTION  IN  EXPOSITION  125 

they  were  quite  sure  of.  The  increase  in  the  percent- 
age of  less-known  words  is  quite  uniform  as  one  moves 
up  the  school,  and  closely  corresponds  to  the  school 
standing  of  the  pupils.  With  those  who  were  quite 
free  in  their  choice  —  that  is,  Group  III  —  there  is  a 
steady  preference  for  the  substantive  element 1  in 
every  case  but  in  that  of  By.  It  is  this  exceptional 
preference  for  a  transitive  element  that  made  me 
qualify  my  general  statement.  There  is  nothing  sur- 
prising in  this  preference  for  the  substantive  elements  ; 
these  form  the  natural  resting-places  of  thought. 
Besides,  the  other  words  that  do  not  carry  a  substantive 
element  depend  for  their  meaning  on  some  relation, 
and  relationship  is  discounted  in  this  case  by  the  fact 
that  the  sounds  are  by  the  conditions  of  the  problem 
presented  in  isolation.  Accordingly,  non-substantive 
words  are  less  likely  to  arise  in  the  mind  as  compared 
with  the  words  indicating  substantive  ideas,  and  on 
that  account  carrying  an  environment  with  them. 

In  the  case  of  homonyms  both  of  which  represent 
substantive  elements,  there  is  a  preferential  back- 
ground in  favour  of  the  more  familiar.  Thus,  Rain 
clearly  outstrips  Reign,  and  that  again  Rein.  We  more 
naturally  think  of  a  containing  vessel  than  of  an  eastern 
potentate  when  we  hear  the  sound  can  (Khan).  So 
with  the  word  vessel  that  has  just  been  used;  when 
taken  by  itself,  its  natural  background  is  the  sea. 

On  the  other  hand,  with  a  given  background  we  have 

1  As  a  matter  of  fact,  I  got  a  higher  percentage  of  Bee's  in  a  post- 
graduate class  (average  age  twenty-three)  than  I  did  with  any  of  the 
undergraduate  classes ;  but  the  numbers  are  too  small  (43  Bee's  from 
a  class  of  70  students)  to  permit  of  our  drawing  any  satisfactory  con- 
clusion. 


126    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

no  hesitation  at  all  in  predicting  the  exact  sense  in 
which  a  given  word  will  be  accepted.  The  background, 
then,  is  of  fundamental  importance  in  suggestion.  In- 
deed, suggestion  often  implies  nothing  more  than  the 
calling  up  of  an  appropriate  background.  The  mind 
does  the  rest  for  itself. 

When  we  come  to  consider  more  exactly  the  nature 
of  suggestion,  we  find  the  usual  differences  of  opinion 
among  psychologists.  To  begin  with,  we  must  keep 
clearly  before  our  minds  that  we  are  concerned  not  with 
pathological  cases  but  with  normal,  healthy  people. 
There  is  a  wholesome  naturalness  that  is  very  attractive 
in  the  view  supported  by  Mr.  W.  Macdougall,1  following 
G.  Tarde,  that  suggestion  may  be  regarded  as  a  direct 
manifestation  of  the  mode  of  behaviour  called  "imita- 
tion." But  while  many  educational  applications  may 
be  made  on  this  basis,  we  are  not  much  helped  by  it 
hi  the  way  of  Exposition.  There  appears  to  be  a  very 
general  agreement  among  psychologists  that  suggestion 
is  ultimately  based  upon  association,  and  it  is  probable 
that  Mr.  Macdougall 's  view  is  not  inconsistent  with  the 
recognition  of  association  as  a  necessary  part  of  the 
development  of  suggestion. 

Wundt  tells  us  that  "suggestion  is  an  association  ac- 
companied by  a  concentration  of  consciousness  on  the 
representations  engendered  [angeregten]  by  the  asso- 
ciation." 2  He  limits  the  application  of  the  term  to 
"only  those  states  of  consciousness  excited  within  us 
which  are  strong  enough  to  resist  —  at  least  for  the 

1  Social  Psychology,  p.  325. 

1  As  I  do  not  have  the  German  text  by  me  at  the  moment,  I  quote 
from  Keller's  French  translation,  Hypnotisme  et  Suggestion  (Alcan), 
p.  72. 


SUGGESTION  IN  EXPOSITION  127 

moment  —  the  contrary  states  of  consciousness  that 
tend  to  destroy  them."  When  we  come  to  educational 
applications  of  the  term,  we  find  that  Professor  P.  Felix 
Thomas  prefers  to  define  it  as:  "The  inspiration  of  a 
belief,  the  true  grounds  for  which  escape  us,  which  with 
greater  or  less  force  tends  of  itself  to  realise  itself."  * 
Thomas  supports  this  view  by  a  reference  to  J.  M. 
Guyau's  definition:  "the  introduction  of  a  practical 
belief  that  of  itself  realises  itself."2  Baldwin  regards 
suggestion  as  "the  tendency  of  a  sensory  or  an  ideal 
state  to  be  followed  by  a  motor  state,"3  and  quotes 
Janet's  formula  :  "a  motor  reaction  brought  about 
by  language  or  perception."4  This  tendency  towards 
realisation  in  action  is  very  commonly  implied  in  the 
use  of  the  word  suggestion;  but  surely  it  is  not  neces- 
sary to  assume  an  impulse  that  issues  in  an  overt  act. 
We  may  surely  suggest  a  line  of  thought  as  well  as  a 
line  of  action.  If  not,  then  suggestion  is  of  very  limited 
use  to  the  mere  expositor.  Sometimes  he  desires  his 
exposition  to  lead  to  a  certain  line  of  action,  as  we  shall 
see  in  the  chapter  on  the  Story  as  Illustration.  But 
it  will  frequently  happen  that  he  desires  no  more  than 
mental  activity.  This,  however,  should  satisfy  the 
psychologists.  It  appears  to  satisfy  Mr.  Macdougall, 
who  gives  us:  "Suggestion  is  a  process  of  communica- 
tion resulting  in  the  acceptance  with  conviction  of  the 
communicated  proposition  in  the  absence  of  logically 
adequate  grounds  for  its  acceptance."  5  Later  in  the 

1  La  Suggestion  son  R6le  dans  I' Education,  p.  20. 

2  Education  et  H&redite,  p.  17. 

3  Mental  Development  in  the  Child  and  the  Race,  p.  105. 

4  Aut.  Psy.,  p.  218. 

6  Social  Psychology,  p.  97. 


128    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

chapter  we  shall  work  up  to  a  fuller  description,  but  in 
the  meantime  it  must  be  understood  that  by  suggestion 
we  mean  the  manipulation  of  the  ideas  of  our  pupil 
so  as  to  produce  a  predetermined  result,  whether  in 
thought  or  action.  For  success  hi  our  work  we  must 
depend  upon  the  Wundtian  concentration  of  conscious- 
ness on  associations. 

The  inspiration  that  leads  to  the  concentration  of  con- 
sciousness may  originate  from  within  or  from  without. 
If  it  comes  from  within,  we  have  what  is  commonly 
called  auto-suggestion.  It  is  sometimes  questioned 
whether  auto-suggestion  is  possible.  The  lay  witness 
quoted  on  page  117  would  certainly  deny  the  possibility. 
For  him  suggestion  necessarily  comes  from  without. 
Professor  Stout  would  at  first  sight  seem  to  be  on  the 
same  side,  if  we  identify  mental  activity  with  the  power 
of  initiative.  According  to  him,  mental  activity  implies 
that  mental  process  is  determined  purely  by  previous 
mental  process.1  But  even  if  we  cannot  produce  a 
single  "bit  of  mental  process  that  is  determined  purely 
from  within,"  it  does  not  follow  that  we  have  no  power 
of  initiation.  We  may  never  get  rid  of  a  certain  resid- 
uum of  stimulus  from  without,  but  all  that  this  im- 
plies is  that  we  are  always  kept  in  touch  with  the  outer 
world,  a  condition  that  is  in  itself  desirable.  We  may 
be  able  to  remain  open  to  all  manner  of  external  sug- 
gestion, and  yet  have  the  power  to  concentrate  our  con- 
sciousness in  the  manner  Wundt  demands;  and  this 
concentration  may  fairly  be  said  to  determine  the  suc- 
ceeding process  in  consciousness.  Now  according  to 
Professor  S.  Alexander:  "  What  I  have  called  mental 
activity  is,  in  the  usual  language  of  psychology,  cona- 

1  Analytical  Psychology,  Vol.  I,  p.  148. 


SUGGESTION  IN  EXPOSITION  129 

tion." 1  Auto-suggestion  may  therefore  be  said  to 
occur  when  we  will  to  concentrate  our  consciousness 
on  certain  associations.  We  know  what  those  asso- 
ciations are,  and  we  have  a  schematic  knowledge  of 
whither  they  are  likely  to  lead.  We  may  not  be  able 
to  call  up  directly  just  the  ideas  we  desire,  but  we  can 
put  ourselves  in  the  most  favourable  situation  to.  en- 
counter them.  We  can  go  where  certain  classes  of 
ideas  are  to  be  found,  and  we  may  have  the  full  as- 
surance that  particular  ideas,  of  which  we  are  at  the 
time  of  beginning  our  quest  only  vaguely  conscious, 
will  by  and  by  sort  themselves  out  and  become  focal. 
Probably  pure  auto-suggestion  is  a  very  rare  phenome- 
non; but  in  any  case  it  does  not  directly  concern  us 
here,  for  the  suggestion  that  we  are  interested  in  is 
that  which  works  from  without,  "foreign  suggestion," 
as  it  is  called  by  Wundt  and  others. 

A  certain  confusion  between  auto-suggestion  and 
foreign  suggestion  sometimes  occurs  through  neglecting 
the  point  of  incidence  of  the  external  influence.  Some- 
times this  is  so  far  removed  from  the  point  at  which 
suggestion  begins  to  act  that  the  subject  has  forgotten 
all  about  the  external  force  (if,  indeed,  he  ever  observed 
it  as  such),  and  regards  his  action  or  thought  as  self- 
suggested.  Some  writers  accordingly  regard  the  term 
auto-suggestion  with  suspicion,  and  one  2  at  least  would 
like  to  use  the  descriptive  term  pseudo-auto-sugges- 
tion, were  it  not  so  intolerably  cumbersome. 

A  knowledge  of  the  working  of  auto-suggestion  may 
no  doubt  help  the  expositor  in  his  preliminary  examina- 
tion of  the  mental  content  of  his  pupils.  A  skilful 

1  Proceedings  of  the  Aristotelian  Society,  1908,  p.  222. 

2  M.  M.  Keatinge,  Suggestion  in  Education,  1907,  p.  55. 

K 


130    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

observer  like  E.  A.  Poe's  Dupin  may  be  able  to  antici- 
pate the  developments  of  a  mental  train  self-origi- 
nated in  another  mind,1  but  as  a  matter  of  fact  the  ex- 
positor is  almost  entirely  interested  in  trains  of  thought 
that  he  has  himself  originated.  His  interest  is  prac- 
tically confined  to  foreign  suggestion,  though  it  has  to 
be  remembered  that  the  false  auto-suggestion  is  in- 
cluded under  this  term.  In  fact,  this  false  auto-sug- 
gestion is  by  far  the  most  effective  form.  It  greatly 
increases  the  power  of  suggestion,  if  what  is  really 
external  suggestion  should  appear  to  the  pupil  to  be 
auto-suggestion.  The  further  back  we  can  throw  the 
incidence  of  the  external  influence  the  better  the  re- 
sults. Indeed,  the  root  principle  of  the  skilful  use  of 
suggestion  is  to  make  the  mind  of  the  pupil  do  as  much 
of  the  work  as  possible.  Why  is  it  that  suggestion  is 
regarded  as  so  much  more  dangerous  in  morals  than 
direct  statement  or  demonstration  ?  It  is  because  sug- 
gestion merely  starts  a  process;  the  mind  carries  it  on, 
and  hi  carrying  it  on  is  apt  to  think  that  it  is  acting 
on  its  own  initiative.  There  is  nothing  so  pleasant  in 
mental  process  as  self-activity,2  and  if  the  mind  can  be 
made  to  feel  that  it  is  carrying  out  its  own  processes  in 
its  own  way,  it  works  with  its  maximum  vigour.  The 
further  back  the  impulse  from  without  can  be  thrown, 
the  greater  the  chance  of  the  pupil  thinking  that  in  a 
given  case  he  is  acting  on  his  own  initiative.  "Hus- 
band, voter,  or  pupil,  they  willingly  follow  a  suggestion 

1  Though  even  here  the  ingenious  Dupin  really  owes  his  success  to 
his  power  of  anticipating  the  effects  on  the  given  mind  of  the  various 
external  stimuli  to  which  he  observes  it  to  be  exposed. 

8  Compare  Whately's  explanation  of  the  fact  that  the  metaphor  is 
more  popular  than  the  simile :  "  All  men  are  more  gratified  at  catching 
the  resemblance  for  themselves  than  in  having  it  pointed  out  to  them." 


SUGGESTION   IN  EXPOSITION  131 

whose  origin  is  so  well  concealed  that  it  seems  to  be 
their  own."  l 

A  pupil  who  can  make  no  headway  with  a  difficult 
rider  in  geometry  may  be  helped  by  the  teacher  bluntly 
suggesting  that  the  solution  of  the  problem  lies  in  the 
demonstration  of  the  equality  of  two  angles,  CDE  and 
RPQ,  which,  from  their  position  on  the  drawing,  do 
not  seem  to  have  any  connection  with  each  other,  and 
certainly  do  not  appear  to  be  equal.  But  if  the  teacher, 
by  shifting  about  the  paper  on  which  the  drawing  is 
made,  is  able  to  place  it  so  that  the  equality  of  the 
angles  is  likely  to  strike  the  pupil's  eye,  he  will  set  up 
a  much  more  vigorous  reaction  than  by  merely  stating 
the  fact.  The  speaker  who  makes  his  conclusion  fol- 
low immediately  on  the  statement  ^  of  two  premises 
saves  time,  no  doubt,  but  does  not  have  the  same  effect 
upon  his  hearers  as  the  man  who  gives  one  premise 
at  one  time  and  the  other  a  little  later,  and  does  not 
give  the  conclusion  at  all,  but  takes  it  for  granted, 
and  uses  it  in  a  further  development  of  his  theme. 
This  is  the  method  of  the  successful  popular  lecturer, 
and  cannot  be  so  usefully  applied  in  the  case  of  diffi- 
cult subjects  presented  to  listless  pupils.  Even  in 
such  adverse  circumstances,  however,  it  will  be  found 
that  an  obvious  inference  is  better  left  to  the  reluctant 
pupil.  After  all,  he  finds  it  less  disagreeable  to  draw 
his  own  obvious  conclusions  than  to  have  them  thrust 
upon  him  from  without. 

From  what  has  gone  before,  it  will  be  seen  that  there 
is  nothing  humiliating  to  the  pupil  in  being  thus  ma- 
nipulated; for  when  all  is  said,  the  success  of  the 
manipulation  depends  entirely  upon  the  nature  and 

1  W.  Mitchell,  Structure  and  Growth  of  the  Mind,  p.  145. 


132    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

content  of  the  pupil-mind.  If  the  pupil  responds  to  the 
external  stimulus,  it  is  because  the  stimulus  appeals  to 
his  nature.  He  responds  to  the  stimulus  because  it 
has  been  so  prepared  as  to  respect  his  individuality. 
All  the  same  there  is  a  very  natural  objection  to  a 
system  that  may  be  in  any  sense  described  as  "Educa- 
tion by  deception."  Dr.  Johnson  is  very  angry  with 
those  who  seek  to  manage  other  people  in  this  way. 
Nobody  likes  to  realise  that  he  is  managed  by  other 
people.  It  is  true  that  Mr.  Keatinge  tells  us  in  his 
book  on  Suggestion  that  "Boys  like  to  be  managed,"  J 
but  he  certainly  knows  too  much  about  boys  to  mean 
that  they  like  to  be  managed  in  this  insidious  way. 
What  he  means  is  probably  just  the  opposite.  Boys 
like  to  feel  that  they  are  in  the  hands  of  a  master, 
though  this,  again,  is  a  little  difficult  to  reconcile  with 
the  stress  he  lays  upon  the  "  contrariant "  characters 
of  the  French  psychologists.  These  characters  are 
said  to  respond  in  the  opposite  sense  to  that  sug- 
gested. In  the  case  of  rigid  contrariants  there  is  no 
difficulty,  since  all  the  suggester  has  to  do  is  to  change 
his  suggestion  from  the  positive  to  the  negative,  and 
the  desired  positive  results  will  follow.  With  the 
more  intelligent  contrariants  the  attempt  to  use  sug- 
gestion resolves  itself  into  a  trial  of  wits  between  the 
suggester  and  the  subject,  each  trying  to  find  out 
what  the  other  really  wants.  It  is  because  of  the  prev- 
alence of  this  contrariant  spirit  that  the  incidence  of 
the  external  suggestion  has  to  be  so  carefully  watched. 
Dr.  Sidis,  in  fact,  goes  the  length  of  regarding  the  con- 
trariant attitude  in  our  unhypnotised  state  as  the  nor- 
mal one,  and  enunciates  the  law  of  human  stubborn- 

1  p.  70. 


SUGGESTION   IN  EXPOSITION  133 

ness:  "Normal  suggestibility  varies  as  indirect  sugges- 
tion, and  inversely  as  direct  suggestion."  l 

An  important  consideration  for  the  teacher  is  that 
suggestion  works  in  only  one  way.  It  is  positive,  not 
negative.  By  suggestion  we  may  cause  another  person 
to  think  or  act  in  a  particular  way;  we  cannot  directly 
cause  him  not  to  think  or  act  in  a  particular  way.  The 
power  of  the  little  word  not  is  greatly  overrated  by  some 
teachers.  They  are  apt  to  think  it  is  more  efficacious 
to  say,  "Don't  use  non  with  the  imperative  in  Latin; 
use  ne,"  than  to  say,  "With  the  Latin  imperative, 
when  we  wish  to  signify  negation,  we  always  use  ne." 
What  we  wish  to  impress  on  the  pupil's  mind  is  that  ne 
is  the  proper  word  to  use  under  certain  circumstances. 
Accordingly,  we  ought  not  to  bring  in  the  word  non  at 
all.  With  regard  to  conduct,  the  word  not  is  very  weak 
as  a  suggestion.  In  the  early  part  of  last  century  there 
was  a  town  and  gown  riot  in  Aberdeen,  and  the  students 
were  not  having  the  best  of  it.  When  they  were  driven 
within  their  own  quadrangle,  and  had  no  available 
weapons  the  old  principal,  disappointed  at  this  result, 
came  out  of  his  house,  and  shaking  his  fist  at  the  stu- 
dents, shouted  that  they  must  not  pull  up  the  palings  to 
use  as  clubs.  Even  had  the  old  gentleman  meant  the 
negation  seriously,  it  would  have  had  no  effect.  There 
was  only  one  suggestion  in  his  remark,  though  there 
were  two  possible  lines  of  conduct. 

Moral  questions  are  not,  however,  urgent  hi  the  use 
to  be  made  of  suggestion  in  Exposition.  Our  interest  is 
rather  in  the  manipulation  of  ideas  than  in  the  particu- 
lar ideas  to  be  manipulated.  For  our  purpose  it  may 
be  permitted  to  regard  suggestion  as  a  force  applied 

1  Psychology  of  Suggestion,  p.  89. 


134    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

from  without  so  as  to  bring  into  action  organised 
powers  latent  in  the  mind  of  another,  and  by  utilising 
our  knowledge  of  their  organisation  to  cause  these 
powers  to  act  in  a  direction  desired  by  the  operator. 
A  static  result  is  not  enough.  If  we  bring  under  the 
notice  of  another  person  some  of  the  elements  of  a  back- 
ground that  we  know  has  previously  existed  in  his 
mind,  the  likelihood  is  that  this  background  will  be 
thereupon  reinstated.  If  this  is  all,  we  have  an  ex- 
ample of  redintegration,  and  the  process  may  not  be 
recognised  by  some  people  as  suggestion  at  all.  It  may 
be  held  that  suggestion  must  lead  to  a  definite  line 
of  mental  activity,  and  not  to  a  mere  reestablishment 
of  a  previous  state.  As  a  matter  of  fact,  the  redintegra- 
tion of  a  background  materially  affects  the  direction 
of  the  immediately  succeeding  activity.  A  reasonable 
description  of  the  function  of  suggestion  in  Exposition 
is  to  say  that  it  is  the  bringing  of  external  influence 
(by  means  of  words,  signs,  pictures,  models,  or  what 
not)  to  bear  upon  a  given  mind  so  as  to  make  it  ap- 
perceive  certain  ideas  in  a  way  predetermined  by  the 
suggester.  Since  apperception  is  an  active  process, 
this  description  should  meet  the  case. 

In  teaching,  as  opposed  to  education,  suggestion  may 
be  regarded  as  the  process  of  initiating  by  more  or  less 
indirect  means  certain  mental  processes  that  have  been 
so  organised  that  when  once  begun  they  are  carried 
out  automatically.  It  may  be  said  to  be  the  tapping  of 
the  forces  stored  up  by  habit,  the  drawing  of  a  cheque 
on  the  paid-up  mental  capital.  We  cannot  suggest 
a  process  that  has  never  before  occurred  in  the  mind. 
We  fail  just  as  we  have  failed  when  we  have  a  cheque 
returned  to  us  from  the  bank  with  the  legend,  "No 


SUGGESTION   IN  EXPOSITION  135 

funds."  The  crudest  example  of  this  class  of  didactic 
suggestion  is  to  be  found  in  the  blunt  giving  of  a  few 
words  that  form  part  of  the  desired  answer.  Plain 
prompting  is  a  kind  of  suggestion.  Teachers  some- 
times adopt  a  sort  of  disguised  prompting  that  seems 
to  give  them  satisfaction  by  saving  them  from  the  dis- 
grace of  having  to  tell  something  that  they  feel  in  honour 
bound  to  elicit.  The  pupils  in  one  case  could  not  be 
persuaded  to  answer  the  question,  "  Which  English 
statesman  was  responsible  for  the  loss  of  the  American 
colonies?"  The  teacher  encouraged  them  by  telling 
them  that  they  knew  quite  well  if  they  would  only 
think.  They  thought;  but  without  success.  At  last 
the  teacher  had  an  inspiration,  and  asked,  "What 
is  the  opposite  of  south?"  She  was  rewarded  with  the 
unanimous  reply,  "Lord  North."  l 

The  teacher  must  not  lose  sight  of  the  fact  that,  in 
addition  to  the  deliberate  and  accidental  suggestions 
of  the  moment,  there  are  certain  general  lines  of  sug- 
gestion that  work  in  a  more  permanent  way.  Most 
of  these  are  what  medical  men  would  call  benevolent, 
but  some  are  malignant,  and  deserve  special  atten- 
tion. It  is  a  desirable  thing  that  when  certain  ideas 
are  recalled  there  should  at  once  arise  by  suggestion 
certain  of  the  important  elements  implied  in  the  con- 
notation of  these  ideas.  But  if  only  trivial  elements 
are  suggested,  there  arises  the  danger  of  a  false  concep- 
tion of  the  idea  as  a  whole.  The  following  extract  from 

1  At  a  drawing-room  meeting  of  a  branch  of  the  Parents'  National 
Education  Union,  a  very  distinguished  London  physician  maintained 
that  he  saw  nothing  wrong  with  this  example  of  the  use  of  suggestion. 
On  the  contrary,  he  believed  it  to  be  an  excellent  illustration,  and  a 
capital  way  of  bringing  the  young  people  to  the  point.  So  hard  is  it 
to  be  efficient  in  two  professions. 


136    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

a  clever  novel l  of  journalistic  and  artistic  life  well 
illustrates  this  permanent  suggestion  of  superficial  ele- 
ments. The  scene  is  a  publishing  office,  and  Mild- 
may,  the  art  editor,  is  discussing  with  Martin,  the 
literary  editor,  the  illustrations  submitted  for  an  Egyp- 
tian story  hi  a  magazine.  Martin  begins :  — 

"Where's  the  Sphinx?" 

"Not  mentioned  in  copy,"  said  Mildmay,  moving  a  little  farther 
behind  Martin's  chair. 

"  Where  are  the  Pyramids  ?  " 

"The  story  contains  no  reference  to  the  Pyramids,"  said  Mildmay, 
quietly. 

"  But  —  but  —  but  —  you  know  better  than  that,  Mildmay ! " 
the  editor  protested,  shocked  and  trembling. 

******* 

"But —  but — my  dear  chap  !  Here's  a  story  about  Egypt,  and 
not  so  much  as  a  Sphinx  or  a  Pyramid  or  anything  at  all  to  suggest 
Egypt  in  it." 

"The  chap  who  drew  that,  Martin,  was  on  the  Condor,  and  at 
Kassassin  and  Tel-el- Kebir." 

"Then  he  ought  to  know  better  than  to  send  us  a  drawing  like 
this." 

An  example  of  the  most  malignant  form  of  the  per- 
manent suggestion  is  to  be  found  in  the  denominators 
of  vulgar  fractions.  These  have  a  peculiarity  that  is 
often  disconcerting.  They  carry  over  to  their  frac- 
tional functions  the  associations  of  their  integer  con- 
nections, with  the  result  that  they  suggest  false 
estimates  of  the  values  of  fractions.  Some  highly 
intelligent  adults  suffer  from  this  permanent  suggestio 
falsi.  Most  of  us  have  come  across  men  who  believed 
that  their  club  was  more  select  than  another,  because 

1  Little  Devil  Doubt:  by  Oliver  Onions,  p.  290. 


SUGGESTION   IN  EXPOSITION  137 

it  was  necessary  to  have  only  a  fifth  of  the  balls 
black  before  rejection  followed,  while  in  the  other  club 
it  required  a  tenth. 

Underlying  the  idea  of  percentage  is  the  permanent 
suggestion  of  considerable  numbers.  Not  infrequently 
illustrations  in  percentages  convey  a  false  impression 
on  this  account  —  not  always  unintentionally.  Un- 
scrupulous persons  quote  the  actual  figures  in  all 
cases  where  they  are  large  and  imposing,  and  when  they 
are  unpleasantly  small  represent  them  by  percentages. 
Grave  injustice  is  sometimes  done  by  the  necessity 
of  expressing  certain  official  returns  in  uniform  tables. 
A  country  teacher  finds,  for  example,  that  her  eighth 
grade  is  listed  as  having  100  per  cent  of  failures  in 
a  certain  examination.  This  reads  like  a  complete 
breakdown  of  the  school,  whereas  all  that  it  means 
is  the  complete  breakdown  of  dull  John  Brown,  who 
happens  to  constitute  the  whole  of  the  eighth  grade  for 
that  year.  Wherever  the  numbers  concerned  are  very 
small,  the  permanent  suggestion  should  be  corrected 
by  a  statement  of  the  actual  figures. 

The  following  quatrain  from  B6ranger's  Let  Gueux 
proved  unexpectedly  difficult  in  an  examination  in 
French : — 

"  Vous  qu'afflige  la  detresse, 
Croyez  que  plus  d'un  h6ros, 
Dans  le  soulier  qui  le  blesse, 
Peut  regretter  ses  sabots." 

On  investigation  I  found  that  the  cause  of  the  trouble 
was  the  force  of  the  permanent  suggestion  of  the  word 
un.  Though  the  students  all  knew,  of  course,  that  the 
word  could  mean  one  as  well  as  a  or  an,  the  suggestion 


138    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

of  an  article  before  a  noun  was  so  overpowering  that 
most  of  the  pupils  had  to  make  the  best  they  could  of  the 
article-sense,  and  as  a  consequence  they  rang  the  varia- 
tions on  "more  of  a  hero."  A  similar  suggestion  played 
havoc  with  a  class  called  upon  to  read  at  sight  a  passage 
which  they  had  not  before  seen  from  the  Twelfth  Book 
of  the 


"  Ardentes  oculorum  orbes  ad  moenia  torsit 
Turbidus,  eque  rotis  magnam  respexit  ad  urbem." 

Since  the  class  had  never  encountered  the  enclitic  que 
in  this  collocation  with  e,  the  horse-suggestion  was  over- 
mastering, supported  as  it  was  by  the  accompanying 
rotis.  The  majority  of  the  pupils  more  or  less  in- 
geniously apostrophised  a  hypothetical  horse. 

It  sometimes  occurs  that  relative  terms  acquire  a 
permanent  suggestiveness  that  leads  to  error.  Towns 
on  the  east  coast  acquire  a  suggestion  of  easterliness. 
Most  people,  for  example,  who  have  not  had  their 
attention  specially  called  to  the  matter,  are  under  the 
impression  that  Edinburgh  is  farther  east  than  Liver- 
pool, which  does  not  happen  to  be  true.  It  is  difficult 
to  believe  that  a  place  "west  of  the  Andes  "may  be 
"east  of  New  York."  The  expositor  must  be  continu- 
ally on  his  guard  against  these  permanent  suggestions. 

We  have  seen  that  the  range  of  suggestion  is  limited 
to  the  mental  content  of  the  pupil.  We  can  suggest  to 
him  new  combinations  of  old  elements  of  experience  ; 
but  we  cannot  suggest  new  experience.  Further,  we 
may  be  quite  aware  of  the  mental  content  of  the  pupil, 
and  yet  be  unsuccessful  in  suggesting  the  proper  ideas. 
We  are  familiar  with  the  story  of  the  American  who  in 
France  did  not  know  the  word  for  mushrooms,  but  made 


SUGGESTION  IN  EXPOSITION  139 

a  sketch  of  one,  and  had  the  mortification  of  being 
offered  an  umbrella.  Palaeographers  tell  us  that  the 
early  iconographs  and  ideographs  are  exceedingly  sug- 
gestive. But  when  tested  by  application  to  modern 
pupils,  it  is  not  found  that  they  make  the  proper 
suggestion.  The  accompanying  two  drawings  are  re- 


FlQ.    1. 

productions  of  early  Chinese  iconographs.  They  are 
merely  different  ways  of  representing  the  same  thing. 
But  though  the  pupil  has  thus  a  double  chance,  it 
becomes  clear  on  making  the  experiment  with  a  class 
that  none  of  the  pupils  can  guess  what  the  drawings 
ought  to  suggest.  Yet  the  palaeographer  tells  us  that 
this  is  regarded  as  "an  exceedingly  clever  abbreviation 
of  a  pictorial  representation  of  flame."  1  The  following 
are  regarded  also  as  particularly  suggestive,  but  to 
English  pupils,  at  any  rate,  they  have  proved  quite 
unintelligible. 


WINDOW  GARDEN  CONSTELLATION 

FIG.  2. 


Accompanied  by  the  interpretation,  all  these  icono- 
graphs are  intelligible  enough,  and  the  symbolism  is 

1  M.  J.B.  Silvestre:  PaUographie  Universelle. 


140    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

quite  apparent,  but  in  themselves  they  suggest  nothing. 
With  the  two  following  drawings  as  they  stand 


FIG.  3. 

I  had  no  success  whatever  in  eliciting  the  meaning 
from  a  class  of  intelligent  students  of  average  age  22. 
But  when  the  help  was  given  that  they  pictured  male 
human  beings  who  stood  in  a  certain  family  relationship 
to  one  another,  and  that  the  silhouettes  were  taken  from 
early  Chinese  writing,  nearly  half  of  the  class  were 
able  to  respond  to  the  suggestion,  and  declared  them 
to  be  father  and  son,  the  suppliant  attitude  of  the  son 
and  the  protecting  attitude  of  the  father  being  quite 
what  one  would  expect,  in  view  of  what  one  hears  of 
the  filial  relation  in  China. 

A  similar  difficulty  in  applying  Suggestion  is  experi- 
enced in  attempting  to  reproduce  in  graphic  form  certain 
states  of  mind.  No  doubt  Sir  Charles  Bell l  and  others 
have  succeeded  in  representing  very  faithfully  some  of 
the  stronger  emotions.  But  unobservant  people  fre- 
quently misunderstand  excellent  graphic  presentations 
of  human  facial  expression,  and  when  we  deal  with  less 
skilful  presentations,  even  intelligent  readers  do  not 
always  respond  successfully  to  the  suggestions  offered. 
M.  Maurice  Castellar,  in  illustrating  the  practical  side  of 
expression,  gives  nine  photographs  of  persons  whose  at- 
titudes and  facial  expressions  are  supposed  to  indicate 

1  Anatomy  of  Expression  in  Painting  (1806). 


SUGGESTION  IN  EXPOSITION  141 

certain  states  of  mind  that  are  set  forth  in  the  explana- 
tory letterpress  that  accompanies  them  in  his  book.1 
There  are  in  all  seventeen  individual  figures,  and  in 
only  four  of  these  did  an  intelligent  class  of  students  hit 
upon  the  state  of  mind  that  was  described  in  the  ex- 
planatory letterpress.  Still,  when  the  letterpress  was 
read,  the  students  were  willing  to  admit  that  the  photo- 
graphs might  be  said  to  represent  quite  well  what  was 
wanted. 

In  the  use  of  suggestion  it  is  obviously  of  importance 
to  discover  the  least  possible  amount  of  energy  to  be 
used  to  produce  a  given  effect.  We  must  seek  out  the 
minimum  suggestible.  It  is  sometimes  discussed  how 
much  of  a  given  complex  must  be  presented  before  the 
whole  is  suggested  to  the  mind.  There  can  be  no 
quantitative  answer.  We  have  no  standard.  Every- 
thing depends  upon  our  familiarity  with  the  complex 
in  question.  The  case  is  sometimes  put:  How  much 
of  the  stag  must  appear  above  the  crest  of  the  hill 
before  the  hunter  is  certain  that  he  is  dealing  with  a 
stag  ?  Clearly,  it  all  depends  on  the  hunter.  There 
are  some  hunters  who  would  require  to  see  pretty  nearly 
the  whole  animal  before  they  would  be  certain,  while 
others  respond  to  suggestion  at  the  first  appearance  of 
the  tip  of  the  antlers. 

With  an  object  for  which  we  are  not  prepared  (the 
stag-hunter  is  assumed  to  have  been  waiting  for  a  stag), 
we  cannot  say  which  element  it  is  that  suggests  the 
complex.  It  does  not  come  to  us  piecemeal,  but  as  a 
whole.  Going  along  a  crowded  street,  we  find  ourselves 
thinking  of  a  certain  friend.  Suddenly  we  become  con- 
scious that  there  he  is,  a  few  steps  in  front  of  us.  The 

1  L'Art  de  VOrateur:  Paris,  1906. 


142    EXPOSITION  AND   ILLUSTRATION  IN  TEACHING 

thought  of  him  has  been  suggested  to  us  by  the  appeal 
of  some  of  his  physical  qualities.  If  we  are  asked  how 
we  knew  it  was  he  from  the  mere  appearance  of  his 
back,  we  find  it  difficult  to  say,  and  what  we  say, 
remember,  is  pure  theory.  The  fact  that  it  is  we  who 
have  seen  and  recognised  the  man  gives  our  evidence 
no  more  authority  than  that  of  anyone  else;  for  the 
recognition  was  not  made  deliberately.  Very  probably 
the  peculiarities  that  we  select  as  distinguishing  our 
friend  had  little  to  do  with  our  recognition.  We  did 
not  observe  this  thing  and  that,  then  reason  out  that  it 
must  be  So-and-so;  So-and-so  sprang  ready-made  into 
our  consciousness.1 

The  fact  seems  to  be  that  if  the  different  elements  of 
a  complex  are  firmly  welded  together,  that  complex  can 
be  suggested  only  as  a  whole.  If  we  wish  to  recall  to 
the  mind  of  another  the  idea  of  a  cow,  we  can  do  so  by 
appealing  to  various  senses,  but  so  soon  as  the  cow 
appears  she  appears  as  a  whole;  it  is  not  a  matter  of 
one  part  appearing  and  being  followed  by  another. 
Further,  the  cow  that  does  appear  is  always  the  same 
cow  for  the  same  mind.  We  have  all  only  one  avail- 
able cow  as  idea.  This  idea  may  be  aroused  at  any 
moment  by  the  sight  of  the  word  cow,  or  by  the  pro- 
nunciation of  that  word,  or  by  the  lowing  of  some  unseen 
animal,  or  by  the  peculiar  odour  that  we  associate  with 
cowsheds,  or  by  the  sound  of  a  peculiar  kind  of  bell. 
However  aroused,  the  resulting  idea  of  cow  in  our  mind 
is  the  same,  if  it  be  allowed  to  develop  to  its  full  extent. 
The  preferred  sense  will  no  doubt  have  its  effect  in  the 

1  For  an  ingenious  theory  that  does  not  agree  with  the  above,  see 
Dr.  W.  T.  Harris's  Psychologic  Foundations  of  Education,  Chaps.  IX 
andX. 


SUGGESTION  IN  EXPOSITION  143 

setting  in  which  the  cow  will  be  found,  but  the  cow 
itself  will  be  the  same,  however  recalled.  To  be  sure, 
this  ideal  cow  is  capable  of  improvement.  Increasing 
experience  of  cows  gives  the  idea  greater  content.  But 
such  a  change  is  gradual.  It  remains  true  that  for  a 
given  stage  the  available  mental  cow  is  constant  for 
the  individual.  For  suggestion  this  is  the  only  cow. 
Changes  can  be  effected  only  by  supplying  means  of 
observation. 

The  question  is  sometimes  raised  whether  we  are 
morally  justified  in  using  suggestion  in  such  a  way 
that  the  person  operated  on  does  not  know  that  sug- 
gestion is  being  used.  Note  that  stress  is  laid  on 
the  fact  that  the  person  affected  is  not  aware  that  he  is 
the  subject  of  suggestion.  But  as  a  matter  of  fact,  if 
the  person  knows  that  suggestion  is  being  used,  it  is  no 
longer  a  case  of  suggestion.  If  we  openly  advise  a 
man  to  follow  a  particular  line  of  conduct,  we  may  be 
said  in  a  certain  sense  to  make  suggestions.  We  may 
even  put  our  advice  in  the  very  form  of,  "Well,  I  would 
suggest  — "  But  this  is  quite  a  different  process  from 
that  we  have  been  considering  in  this  chapter,  —  the 
problem  of  the  sanction  of  suggestion  solvitur  ambu- 
lando.  Whether  we  will  or  no,  we  are  continually 
using  suggestion  in  the  sense  in  which  we  understand 
it  here.  It  is  true  that  we  may  use  it  sometimes  more, 
sometimes  less,  deliberately.  But  even  so,  the  problem 
has  to  be  carried  a  step  farther  back  before  it  is  worth 
discussing.  Not  the  use  of  suggestion,  but  the  pre- 
paring the  mind  for  suggestion,  is  the  responsible 
work.  Suggestion  is  powerless  to  do  anything  but  set 
in  motion  forces  that  are  latent  but  none  the  less  ex- 
istent. The  sight  of  means  to  do  ill  deeds  makes  ill 


144    EXPOSITION  AND   ILLUSTRATION   IN  TEACHING 

deeds  done,  only  when  the  ill  deeds  are  already  within 
the  mental  content  of  the  person  tempted.  Sugges- 
tion is  powerful  only  in  so  far  as  it  follows  the  laws  and 
takes  account  of  the  content  of  the  mind  operated  upon. 
This  is  the  psychological  explanation  of  the  saying  that 
to  the  pure  all  things  are  pure.  No  amount  of  sugges- 
tion can  evoke  from  the  mind  ideas  that  are  not  there. 

Still,  it  cannot  be  denied  that  suggestion  is  capable 
of  illegitimate  applications.  It  is  significant  that  the 
word  is  only  now  emerging  from  a  very  discreditable 
association  in  the  dictionary,  and  even  still  the  adjec- 
tive suggestive  connotes  a  special  and  particularly 
vile  class  of  things  to  be  suggested.  But  the  fact  that 
the  process  is  recognised  as  preeminently  dangerous 
is  only  an  argument  the  more  for  the  educator  seizing 
this  specially  powerful  means  of  influencing  his  pupils. 
If  it  can  so  easily  lead  pupils  wrong,  it  is  surely  our  duty 
to  learn  how  to  use  it  on  the  side  of  right.  There  is 
no  reason  why  evil  should  monopolise  suggestion. 

From  the  moral  standpoint,  the  purpose  of  education 
is  really  to  make  the  pupil  suggestible  to  certain  in- 
fluences. The  good  boy  is  the  boy  who  responds  to 
suggestion  in  the  way  that  his  teacher  regards  as  right. 
In  intellectual  instruction  the  same  may  be  said.  The 
boy  who  knows  a  subject  really  well  is  the  boy  who  can 
be  depended  upon  to  respond  loyally  to  suggestion  in 
his  subjects.  Suggestion,  while  a  valuable  means  of 
Exposition,  is  al^o  in  itself  one  of  the  goals  of  intellec- 
tual education. 


CHAPTER  VI 
CONDITIONS  OF  PEESENTATION 

PBESENTATION  is  one  of  the  Five  Formal  Steps  that 
are  now  the  common  property  of  all  who  deal  with 
method  in  teaching. 

The  very  name  Formal  Steps  implies  two  underlying 
assumptions.  It  takes  for  granted,  in  the  first  place,  that 
it  is  possible  to  separate  form  from  matter  in  teaching. 
One  may  be  a  little  surprised  to  find  in  these  steps  that 
originated  with  Herbart  this  emphasis  on  the  formal 
side.  The  usual  criticism  against  him  and  his  followers 
is  that  they  attach  undue  importance  to  the  nature  of 
the  matter  to  be  presented  to  the  pupil.  According 
to  them  a  man  is  what  he  is  because  he  knows  what 
he  knows.  When  we  find,  then,  that  the  Herbartians 
commit  themselves  to  form  at  all,  we  may  take  it  for 
certain  that  the  matter  to  be  taught  is  not  neglected. 
The  Formal  Steps  are  a  statement  of  the  process  of 
teaching,  with  the  minimum  reference  to  the  nature  of 
the  matter  to  be  taught.  We  can  never  entirely  elimi- 
nate consideration  of  the  subject-matter  of  instruction, 
but  in  the  formal  steps  it  is  maintained  that  the  separa- 
tion of  form  and  matter  has  been  carried  to  the  ulti- 
mate point.  By  following  these  steps  it  is  claimed  that 
the  teacher  will  best  guide  the  pupil  in  the  process  of 
learning,  and  that  with  the  minimum  consideration  of 
the  nature  of  the  matter  to  be  learned. 

L  145 


146    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

•  The  second  assumption  is  that  instruction  should 
proceed  by  definite  steps.  Comenius  warns  us  with 
some  energy,  and  not  a  little  repetition,  that  nature 
never  proceeds  by  leaps,  but  always  by  steps.  Herbart 
has  taken  this  warning  to  heart,  and  has  systematised 
the  steps  hi  teaching  that  he  believes  nature  would  have 
us  follow.  We  must  not  confound  the  need  for  step- 
wise  progression  with  the  speed  with  which  progress 
is  accomplished.  Whatever  nature  may  do,  children 
certainly  sometimes  appear  to  proceed  by  leaps  in  their 
thinking.  We  often  accuse  them  of  jumping  to  con- 
clusions. But  this  does  not  show  that  they  have  not 
proceeded  stepwise,  unless  by  stepwise  we  mean  that 
every  step  must  be  deliberately  taken.  The  fact  that 
I  go  upstairs  three  steps  at  a  tune  does  not  prove  that 
I  am  not  going  upstairs.  I  proceed  stepwise,  though  I 
take  big  steps,  and  though  I  do  not  take  every  indi- 
vidual step  that  I  might.  The  clever  pupil  may  pass 
over  many  steps  that  the  teacher  may  feel  called  upon 
to  deal  with  hi  class,  and  the  stupid  pupil  frequently 
requires  additional  steps  to  be  interpolated  between 
what  may  be  regarded  as  the  normal  steps;  but  both 
kinds  of  pupils  are  proceeding  along  in  the  same  direc- 
tion, covering  the  same  course,  though  the  one  has  to 
touch  the  ground  much  more  frequently  than  does  the 
other.  The  number  of  steps  to  be  taken  is  one  ques- 
tion, —  and  in  itself  a  very  important  one,  particularly 
in  relation  to  class-work,  —  the  order  in  which  these 
steps  have  to  be  taken  is  another.  It  is  mainly  with 
the  order  of  the  steps  that  Herbart  deals  when  he 
speaks  of  the  Formal  Steps. 

As  a  matter  of  fact,  Presentation  does  not  occur  among 
the  steps  originally  suggested  by  Herbart.     These  were 


CONDITIONS  OF  PRESENTATION  147 

only  four,  named  respectively,  Clearness,  Association, 
System,  Method.1  These  names  are  not  very  suitable 
as  descriptions  of  processes,  so  later  writers  have  in- 
troduced certain  changes.  The  first  step,  that  which 
leads  to  clearness  in  the  pupil's  mind,  is  really  made  up 
of  two  processes,  and  may  therefore  be  regarded  as  a 
double  step.  The  first  of  these  processes  consists  of 
analysis:  the  contents  of  the  pupil's  mind  must  be 
analysed  so  that  he  may  be  prepared  to  receive  the  new 
matter.  The  second  consists  in  a  synthesis  of  the  new 
matter  with  the  old.  The  analytic  step  has  been  named 
preparation,  and  the  synthetic,  presentation.  It  may 
not  be  amiss  here  to  emphasise  the  fact  that  prepara- 
tion in  this  sense  means  preparation  of  the  pupil's  mind, 
not  the  teacher's.  There  has  been  a  good  deal  of  dis- 
cussion about  the  naming  of  the  different  steps.  Prob- 
ably the  most  widely  accepted  nomenclature  of  the 
five  steps  now  generally  recognised  is,  Preparation, 
Presentation,  Association,  Generalisation,  and  Applica- 
tion.2 

It  is  sometimes  held  that  in  the  first  two  steps  we  are 
working  on  the  perceptual  plane.  Certain  elements  of 
our  past  experience  have  been  combined  with  certain 
new  elements;  but  that  is  all.  The  new  wholes  thus 
formed  are  yet  mere  units,  though  they  are  in  them- 
selves complex.  They  must  now  be  brought  into  rela- 
tion with  other  wholes.  At  this  stage  we  are  not  very 
particular  which  other  simple  or  complex  units  they 
are  brought  into  relation  with.  What  we  want  is  to 

1  Allgemeine  Padagogik,  Book  II,  Chap.  2. 

2  For  a  tabular  presentation  of  the  various  classifications  of  the 
Steps  by  the  followers  of  Herbart,  see  p.  139  of  Charles  de  Garmo's 
Herbart  in  the  Great  Educators  Series. 


148    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

bring  the  new  unit  into  relation  with  as  many  other 
units  as  we  have  at  our  disposal.  To  bring  this  about, 
the  best  means  is  easy  discussion,  not  in  the  sense  of 
argument,  but  rather  in  that  of  free  conversation.  The 
teacher  can  work  up  the  association  of  a  subject  in 
different  ways.  He  may  suggest  as  many  similar  ideas 
as  he  can,  and  thus  encourage  comparison,  with  a  view 
to  bringing  out  resemblances.  Or  he  may  call  up  as 
many  contrary  ideas  as  the  experience  of  his  pupils  sup- 
plies, and  thus  lead  to  arrest  by  force  of  contrast  within 
the  same  field.  Or  he  may  change  the  point  of  view 
from  which  the  newly  presented  ideas  are  to  be  viewed, 
and  thus  show  them  up  against  different  backgrounds. 
The  purpose  of  this  third  formal  step  —  called  Associa- 
tion —  is  to  find  the  true  place  of  the  new  combination 
in  the  nature  of  things  as  represented  by  the  present 
content  of  the  mind  in  question.  The  associations 
formed  at  this  stage  may  be  of  a  purely  accidental 
character.  Naturally  most  of  the  ideas  with  which 
the  newly  acquired  elements  are  compared  or  contrasted 
have  something  in  common.  But  in  turning  over  ideas 
in  the  mind,  combinations  of  purely  disparate  ideas  must 
frequently  be  formed.  The  complexes  thus  formed 
are  at  this  stage  not  of  primary  consequence,  though 
they  should  all  be  able  to  bear  the  test  of  comparison 
with  an  objective  standard.  What  is  at  present  aimed 
at  is  the  familiarising  of  the  new  elements  with  their 
surroundings  in  the  mind. 

The  next  step,  called  Generalisation,  goes  further. 
Like  association  it  implies  the  grouping  together  of  the 
elements  of  experience,  but  this  time  the  grouping  is  no 
longer  a  matter  of  chance  or  arbitrary  choice.  We 
have  to  advance  from  mere  grouping  to  system. 


CONDITIONS  OF  PRESENTATION  149 

Association  supplies  us  with  the  materials  for  forming 
concepts,  but  it  is  the  work  of  the  Generalisation 
step  to  develop  the  concept.  This  is  why  the  step 
is  variously  named  System,  Concentration,  and  Gener- 
alisation. Underlying  each  of  the  elements  joined  to- 
gether at  the  step  of  Association,  there  is  a  deeper 
meaning  than  appears  at  the  first  casual  glance.  At 
the  associational  stage  we  regard  this  chair  and  that  as 
self-existing  objects.  They  are  no  doubt  related  to 
other  objects  inasmuch  as  they  all  coexist  in  time  and 
space.  But  the  essential  oneness  of  all  chairs  is  really 
perceived  at  quite  an  early  stage.  The  child  behaves 
intelligently  towards  a  chair  that  he  has  not  seen  before 
if  he  has  already  had  dealings  with  a  few  chairs,  or  even 
with  only  one  if  the  new  chair  is  not  too  unlike  the  first. 
But  he  does  not  realise  this  oneness  till  he  has  had  it 
brought  to  consciousness  by  a  process  of  generalisation. 
The  process  of  generalisation  is  apparently  a  very 
complicated  one,  and  when  we  reflect  that  it  implies  as 
a  necessary  preliminary  the  process  of  abstraction,  we 
seem  to  have  ruled  it  out  of  court  altogether  so  far  as 
young  pupils  are  concerned.  But  as  a  matter  of  fact 
it  is  not  necessary  to  go  through  the  complete  process 
of  philosophical  generalisation  in  the  junior  school- 
room. Without,  of  course,  knowing  of  the  existence  of 
such  a  thing  as  the  self-conscious  level,  the  very  young- 
est pupils  generalise  with  ease.  It  is  indeed  the  fatal 
ease  with  which  they  generalise  that  calls  for  such  care- 
ful treatment.  It  is  not  the  difficulty  in  getting  them 
to  generalise  that  need  concern  the  teacher,  but  the 
difficulty  of  preventing  them  from  generalising  wildly. 
Children  begin  to  generalise  in  their  nurse's  arms, 
When  a  child  calls  a  cat  a  bow-wow,  or  a  dog  a  pussy, 


150    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

we  say  he  generalises  rashly.  As  a  matter  of  fact  he  is 
guilty  of  an  undistributed  middle.  But  the  appeal  to 
reason  at  this  stage  is  out  of  the  question.  Not  rea- 
soning is  wanted,  but  experience. 

To  avoid  rash  generalisations  the  association  step 
must  be  carefully  made.  Ordinary  experience  secures 
that  in  the  great  majority  of  cases  the  association  step 
is  sufficiently  elaborated  to  prevent  at  least  such  rash 
generalisations  as  are  dangerous.  In  actual  teaching 
the  association  step  can  be  so  manipulated  as  to  meet 
the  special  needs  of  the  generalisation  about  to  be  made 
in  the  next  step.  For  instance,  if  the  teacher  is  afraid 
that  the  pupils  are  likely  to  fall  into  Sir  Thomas 
Browne's  rash  generalisation  and  maintain  that  no 
quadruped  lays  eggs,  the  conversation  at  the  associa- 
tion stage  may  be  directed  to  frogs,  crocodiles,  and  such 
troublesome  exceptions  to  an  otherwise  unobjectionable 
generalisation.  The  value  of  the  conversational  method 
lies  in  the  fact  that  it  turns  attention  in  a  great  variety 
of  directions,  and  thus  brings  forward  collocations  of 
facts  that  produce  healthy  contradictions,  and  prevent 
generalisations  that  otherwise  might  have  passed  mus- 
ter. The  greater  the  knowledge  the  teacher  possesses 
of  the  content  of  the  minds  of  his  pupils,  the  more 
effectively  can  he  direct  the  course  of  the  association 
step.  But  even  with  the  best-informed  teacher  there 
must  always  remain  a  vast  unexplored  region  of  the 
pupil-mind  which  can  be  best  dealt  with  by  the  free 
course  of  conversation. 

Once  the  generalisation  has  been  obtained,  there  is 
room  for  ingenuity  in  the  way  of  fixing  it  in  the  memory 
of  the  pupils.  The  apt  phrase,  the  epigrammatic 
definition,  the  broad  general  rule  are  all  here  in  place. 


CONDITIONS  OF  PRESENTATION  151 

Even  the  moral,  if  well  expressed,  may  have  its  claims 
recognised  on  the  condition  that  it  has  been  worked 
for  by  the  pupil.  When  once  the  moral  has  been 
worked  for  and  expressed  in  the  pupil's  blundering 
language,  there  can  be  no  harm  in  translating  his  halt- 
ing sentences  into  crisp  English. 

The  final  step  is  named  Application.  We  must  not 
rest  content  with  imparting  facts,  correlating  them 
with  facts  already  known,  and  deducing  from  them  the 
underlying  meaning.  They  remain  as  mental  lumber 
till  they  are  applied  in  actual  life.  It  is  one  thing  to 
know:  it  is  quite  another  to  be  able  to  use  knowledge. 
A  very  useful  classification  of  our  pupils  may  be  made 
on  this  point.  There  are  those  who  have  much  more 
knowledge  than  they  can  make  use  of,  and  those  who 
could  make  use  of  much  more  knowledge  if  they  had  it. 
We  are  familiar  in  school,  and  perhaps  more  familiar 
still  in  ordinary  life,  with  the  person  that  can  make  a 
little  knowledge  go  a  very  long  way,  and  also  with  the 
person  that  is  full  of  knowledge  and  cannot  make  any 
use  of  it.  A  good  method  of  Exposition  must  do  some- 
thing towards  bringing  these  two  extremes  together. 
The  earlier  of  the  formal  steps  provide  the  knowledge 
in  the  best  form :  the  final  step  sees  that  this  knowledge 
gets  a  field  on  which  it  can  be  exercised. 

It  is  quite  possible  for  the  pupil  to  have  a  piece  of 
knowledge  without  being  at  all  able  to  use  it.  In 
several  hundred  classes  I  have  held  up  a  six-inch  foun- 
tain pen  and  invited  the  pupils  to  tell  me  how  long 
a  half  of  three-quarters  of  it  was.  I  had  but  a  small 
percentage  of  answers.  Yet  the  moment  the  prob- 
lem was  stated  on  the  blackboard  as  "Find  the  value 
of  one-half  of  three-fourths  of  six  inches,"  most  of  the 


152    EXPOSITION  AND   ILLUSTRATION  IN  TEACHING 

pupils  were  indignant  at  being  asked  such  an  easy  one.1 
This  final  step,  then,  is  the  place  for  exercises  of  all 
kinds.  Till  the  pupil  has  applied  his  knowledge  in  some 
way,  it  is  not  really  knowledge  to  him.  It  is  something 
inert,  dead,  useless.  When  the  application  step  has 
been  completed,  the  knowledge  is  living;  fact  has  been 
turned  into  faculty.  This  may  not  unfitly  be  described 
as  the  ami  of  the  whole  series  of  formal  steps.  They 
have  served  their  purpose  if  they  have  so  presented  and 
manipulated  the  facts  that  they  have  become  faculty. 

Two  common  lines  of  error  in  the  application  of 
these  Formal  Steps  have  done  much  to  diminish  their 
usefulness.  . 

In  the  first  place  there  is  a  tendency  among  the  more 
matter-of-fact  teachers,  those  who  are  just  a  little  above 
the  rule  of  thumb,  to  emphasise  unduly  the  second  step. 
To  such  ultra-practical  teachers  Presentation  is  the 
only  step  that  need  be  seriously  considered.  It  is  the 
one  bright  gleam  of  light  in  an  otherwise- dark  system. 
To  present  new  ideas  to  the  pupil's  mind:  that  is  teach- 
ing. All  the  other  steps  are  more  or  less  pedantic 
refinements,  but  Presentation  is  something  real,  some- 
thing that  commends  itself  to  a  man  of  common  sense. 
Yet  as  a  matter  of  fact  complete  Presentation  is  pos- 
sible only  in  so  far  as  all  the  other  steps  are  taken.  It 
may  seem  trifling  to  say  that  the  mind  can  accept  only 
what  it  has  been  prepared  for;  but  the  constant  neglect 
of  this  commonplace  is  the  cause  of  much  unsuccessful 
teaching.  The  practical  teacher  is  right  in  seizing 
upon  Presentation  as  being  the  most  important  of 

1  As  illustrating  the  power  of  the  mere  form  of  expression,  it  is 
interesting  to  note  that  I  got  somewhat  better  results  when  I  asked 
for  one-half  than  I  did  when  I  asked  for  a  half. 


CONDITIONS  OF  PRESENTATION  153 

the  five.  It  may  not  unreasonably  be  maintained 
that  the  whole  five  steps  are  only  different  aspects  of 
Presentation  in  its  wide  sense.  But  we  must  not  con- 
fuse a  special  aspect  of  Presentation  separated  off  from 
the  others  and  labelled  the  second  step,  with  Presenta- 
tion as  a  name  for  the  whole  process  that  cannot  be 
completed  without  the  whole  five  steps. 

The  view  that  all  teaching  resolves  itself  into  the 
direct  giving  of  information,  the  telling  the  pupil 
something  new,  has  produced  a  natural  reaction  which 
leads  to  error  in  the  application  of  presentation,  or 
rather  by  the  elimination  of  presentation.  From 
their  studies  in  theory  young  teachers  are  inclined  to 
avoid  anything  in  the  form  of  direct  presentation. 
The  second  step,  while  still  monopolising  their  atten- 
tion, is  regarded  with  suspicion.  What  is  contemp- 
tuously called  " telling"  is  regarded  by  these  young 
teachers  as  in  the  highest  degree  unintelligent  and  un- 
scientific, and  they  fall  into  ludicrous  errors  in  their 
efforts  to  avoid  it.  Everything  must  be,  in  the  words 
of  their  text-books,  "  elicited  from  the  pupil  by  skilful 
questioning."  They  do  not  realise  that  there  are  two 
kinds  of  knowledge:  one  that  must  be  communicated 
directly,  and  another  that  may  be  worked  up  from 
materials  already  in  the  mind.  We  want  very  badly 
a  couple  of  words  to  keep  these  two  kinds  of  know- 
ledge from  getting  mixed.  I  cast  covetous  eyes  on  the 
two  words  information  and  instruction.  The  first 
would  very  well  represent  the  communication  of  new 
facts,  the  second  might  stand  for  the  rearrangement  of 
facts  that  are  already  known  to  the  pupil-mind  in  one 
way,  but  that  by  being  recombined  may  produce 
knowledge  that  was  latent,  if  you  like,  but  that  certainly 


154    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

would  never  have  come  to  light  at  that  stage,  but  for 
the  intermediation  of  the  teacher.  It  is  information 
to  tell  me  the  Japanese  word  for  a  tree.  If  I  do  not 
happen  to  know  the  word,  no  amount  of  skilful 
questioning  will  ever  elicit  it  from  me.  On  the  other 
hand  the  generalised  formulae  of  Euler's  Theorem  * 
may  be  said  to  be  implicit  in  the  pupil's  mind  before 
he  approaches  the  problem.  All  the  teacher  has  to  do 
is  to  arrange  that  certain  ideas  shall  be  grouped  in  a 
particular  way,  and  the  formulae  issue  of  themselves. 
The  meaning  of  instruere,  that  our  dealings  with  Caesar 
have  familiarised  us  with,  comes  in  very  appositely 
here.  The  general  draws  up  the  line  of  battle,  now 
making  one  formation,  now  another.  In  every  case 
the  men,  like  the  ideas,  are  given.  Information  is  as 
different  from  Instruction  as  recruiting  is  from  drilling. 
The  second  error  in  the  application  of  the  Formal 
Steps  is  just  the  opposite  of  what  we  have  been  consider- 
ing. Instead  of  being  tempted  to  overestimate  one  of 
the  Steps  and  neglect  the  others,  the  teacher  may  be 
impelled  to  insist  too  rigidly  on  the  individual  rights 
of  each  step ;  in  other  words,  to  insist  pedantically  on  the 
Steps,  the  whole  of  the  Steps,  and  nothing  but  the  Steps. 
For  long,  students  in  the  training  colleges  of  Great  Brit- 
ain arranged  their  Notes  of  Lessons  in  three  columns, 
at  the  top  of  which  stood  the  words  Heads,  Matter, 
Method,  respectively.  The  Formal  Steps  came  along 
and  introduced  a  welcome  elasticity  into  the  form  of 
note-making.  Unfortunately  the  new  system  is  rapidly 
settling  down  into  the  old  rigidity.  The  student  first 
of  all  makes  the  mistake  that  every  lesson  must  exem- 
plify the  whole  of  the  Steps,  forgetting  that  the  teaching 

1  See  p.  34. 


CONDITIONS  OF  PRESENTATION  155 

unit  does  not  necessarily  coincide  with  the  lesson  unit. 
It  may  take  several  lessons  to  complete  the  cycle  of 
the  Steps  in  respect  of  some  important  section  of  a 
subject.  Besides,  all  the  Steps  are  not  always  of  the 
same  importance.  Particularly  the  two  steps,  Associa- 
tion and  Generalisation,  have  very  different  values 
according  to  circumstances.  It  is  no  uncommon  ex- 
perience to  find  a  student  coming  to  her  Mistress  of 
Method  with  the  distressing  news  that  she  "simply 
can't  get  a  generalisation  for  this  lesson."  As  a  matter 
of  fact,  the  one  important  thing  is  that  a  subject  should 
be  so  presented  that  when  the  lesson  is  over  the  new 
matter  shall  have  been  worked  into  the  very  warp 
and  woof  of  the  mental  content  of  the  pupils.  In  the 
process  the  Formal  Steps  give  very  useful  guidance,  but 
that  guidance  must  be  of  a  general  kind.  Application, 
for  example,  need  not  be  kept  entirely  to  the  end  of  the 
process.  Frequently  it  comes  in  very  appositely  along 
with  Association.  Sometimes  generalisation  may  force 
itself  in  before  association  has  had  tune  to  complete 
its  work,  and  sometimes  there  may  be  no  need  of  gener- 
alisation at  all.  The  Steps  meet  the  case  of  the  normal 
mind  under  normal  conditions,  but  they  have  been 
formed  on  experience  of  how  the  mind  acts,  and  are  not 
something  above  the  mind,  and  therefore  something 
that  the  mind  must  obey.  Most  people  who  have  had 
to  do  with  the  training  of  teachers  have  had  experience 
of  the  complaint  expressed  to  a  class  that  is  answering 
ahead  of  what  the  teacher's  notes  arranged  for:  "But 
you  don't  know  that  yet."  This  means  that  the 
pupils  have  anticipated  what,  according  to  the  teacher's 
calculations,  is  not  due  for  several  questions  yet.  In 
such  cases  it  may  still  be  desirable,  for  the  sake  of  the 


156    EXPOSITION   AND    ILLUSTRATION   IN  TEACHING 

duller  members  of  the  class,  that  the  teacher  should 
insist  on  going  through  what  he  had  intended.  But 
he  must  realise  that  there  is  no  absolutely  fixed  rate 
at  which  pupils  learn. 

All  the  same,  it  is  not  a  matter  of  indifference  in  what 
order  facts  are  presented  to  the  pupils.  Old  facts  that 
have  to  be  recalled,  and  new  facts  that  have  to  be  pre- 
sented, cannot  be  put  forward  haphazard.  It  may 
be  impossible  to  lay  down  any  fixed  law  according  to 
which  presentation  must  always  be  made,  for  some- 
times one  fact  and  sometimes  another  may  be  the  best 
to  bring  forward  first.  Everything  depends  upon  the 
mental  content  of  the  pupil,  and  the  purpose  the  teacher 
has  in  view  at  the  tune.  It  is  conceivable  that  the 
same  matter  might  have  to  be  presented  by  the  teacher 
in  quite  a  different  order  to  the  same  class,  according 
as  the  lesson  is  to  be  given  at  the  beginning,  the  middle, 
or  the  end  of  a  given  session.  Indeed,  so  important  is 
this  question  of  order,  that  as  soon  as  we  have  dealt 
with  some  other  of  the  conditions  of  presentation,  we 
shall  devote  a  couple  of  chapters  to  it. 

One  of  the  most  popular  problems  in  examination 
papers  for  teachers  is  to  work  out  the  relation  between 
the  inductive  and  the  deductive  methods  of  teaching. 
The  orthodox  answer  seems  to  be  that  we  should  begin 
with  the  inductive,  and  end  with  the  deductive.  But 
obviously  the  two  methods  cannot  be  dissociated  in  a 
wholesale  way.  No  doubt  in  dealing  with  a  particular 
part  of  a  subject  one  method  or  the  other  has  the  prefer- 
ence, but  when  we  view  the  field  of  school  work  as  a 
whole,  we  find  that  there  is  a  place  for  both,  all  through 
the  pupil's  course.  Speaking  generally,  new  matter  is 
acquired  by  inductive  methods  and  applied  by  deduc- 


CONDITIONS  OF  PRESENTATION  157 

live.  But  in  the  application  by  means  of  deductive 
methods  we  put  ourselves  hi  the  way  of  learning  at 
least  some  new  matter  as  well  as  establishing  what  we 
have  already  mastered.  It  is  not  that  we  are  inductive 
at  the  beginnings  of  our  subjects  and  deductive  later 
on.  The  two  processes  interlace  even  at  the  beginning. 
Some  law  must  be  laid  down,  some  datum  given  even  at 
the  start.  Thus  in  making  a  beginning  of  the  teaching 
of  Latin,  we  may  either  give  a  few  rules  of  construction 
and  a  few  Latin  words  with  their  meanings,  and  set  our 
pupils  to  read  a  bit  of  Latin;  or  we  may  give  our 
pupils  a  bit  of  Latin  and  tell  them  its  general  meaning, 
then  set  them  to  find  out  the  meaning  of  the  individ- 
ual words  and  to  learn  the  meaning  of  case,  number, 
person,  and  what  not,  from  their  experience  of  the  way 
in  which  words  behave  in  Latin  passages.  The  first 
method  would  be  generally  described  as  deductive,  the 
second  as  inductive.1  Obviously  there  are  inductive 
and  deductive  elements  in  both.  The  alternation 
between  the  two  methods  characterises  the  whole 
course  by  which  the  boy  acquires  a  mastery  over  his 
subject. 

This  alternation  of  the  different  methods  is  paralleled 
by  a  different  form  of  rhythm  that  is  characteristic  of 
Exposition.  This  is  the  alternation  between  the  con- 
centration beat  and  the  diffusion  beat.  Viewed  from 
the  standpoint  of  psychology,  this  is  usually  regarded 
as  the  rhythm  of  attention.  But  it  is  not  a  matter 
merely  of  greater  and  less  attention,  but  rather  a  change 
in  the  area  of  the  field  within  which  attention  is  dis- 
tributed. There  is  a  tendency  among  teachers  to 

1  For  the  Inductive  Method  in  Latin  teaching,  see  Bennett  and 
Bristol's  The  Teaching  of  Latin  and  Greek,  p.  80  ff. 


confound  intensity  of  attention  with  the  narrowness 
of  the  range  within  which  it  is  exercised.  A  pupil 
may  attend  as  intently  to  a  wide  field  that  he  has 
under  observation  as  he  does  in  concentrating  his  atten- 
tion on  the  tip  of  a  blade  of  grass  in  that  field.  In 
practice  it  is  found  that  there  is  need  for  continual 
change  of  what  may  be  called  the  focus  of  attention,  and 
of  this  changing  focus  the  expositor  must  take  careful 
heed.  Microscopic  work  affords  us  a  useful  parallel. 
The  observer  usually  begins  by  using  the  low  power, 
say  70,  to  get  a  general  idea  of  the  specimen  under 
examination.  By  and  by  he  wants  to  get  a  more 
detailed  view  of  some  part.  Accordingly  he  uses  a 
higher  power  and  turns  on  perhaps  the  350  objective. 
Some  part  of  the  new  field  he  desires  to  examine  in 
still  further  detail,  and  in  consequence  he  uses  the  700 
objective.  But  while  working  with  these  high  powers, 
he  begins  to  get  a  distorted  view  of  the  object  as  a 
whole,  and  to  correct  this  he  returns  to  the  lowest  power 
of  all.  It  is  because  of  this  need  for  continual  change 
from  one  power  to  another  that  the  double  nozzle  and 
the  multiple  nozzle  are  supplied  to  microscopes,  so 
that  with  the  minimum  outlay  of  time  the  field  of 
vision  may  be  changed  according  to  the  degree  of  detail 
the  observer  desires. 

In  Exposition  we  are  continually  changing  our  focus, 
and  there  is  a  certain  danger  that  the  expositor's  focus 
may  change  without  a  corresponding  change  on  the 
part  of  the  pupil.  The  Expositor  may  be  working  with 
the  700  objective  while  the  pupil  is  working  with  the 
70.  The  tendency  in  Exposition  as  in  microscopic  work 
is  to  use  the  higher  powers  too  freely,  or  rather  too 
frequently,  without  reference  to  the  low  powers.  It 


CONDITIONS  OF  PRESENTATION  159 

is  natural  to  suppose  that  the  higher  the  power,  the 
more  the  pupil  will  learn.  There  is  the  misleading 
"permanent  suggestion"1  of  the  word  thorough.  To 
know  a  thing  thoroughly  is  generally  understood  to 
mean  to  know  it  in  great  detail.  But  it  is  not  unusual 
to  find  a  person  who  knows  a  subject  in  great  detail 
and  yet  has  no  command  over  that  subject,  because 
he  has  not  correlated  the  details  to  the  broad  general 
principles.  In  Exposition  the  teacher  must  concentrate 
now  on  this  point,  now  on  that;  but  he  must  never  fail 
to  correlate  the  minute  points  of  the  concentration  beat 
with  the  broad  outlines  of  the  diffusion  beat.  He  must 
learn  from  the  painter  who  goes  close  up  to  his  canvas 
to  peer  into  it  and  put  in  a  delicate  stroke  or  two  only 
to  step  back  a  few  paces  so  as  to  get  the  general  effect. 
The  painter  is  attending  as  keenly  at  the  long  range  as 
he  is  at  the  short  one,  and  doing  quite  as  valuable 
work. 

It  is  obviously  of  the  first  importance  that  expositor 
and  pupil  should  be  at  each  moment  working  with  the 
same  power.  This  is  sometimes  secured  by  the  ex- 
positor making  use  of  certain  conventional  expressions, 
such  as  "speaking  very  generally,"  "taking  a  wider 
view  we  find,"  "coming  now  to  details  we  see."  Apart 
from  specific  verbal  cautions,  the  best  way  to  maintain 
identity  of  power  is  to  use  the  material  in  such  a  way 
as  to  lead  to  difficulties  if  it  is  presented  along  with 
material  that  belongs  to  a  different  grade.  This  may 
be  best  illustrated  by  the  case  of  history,  where  we  have 
the  possibility  of  a  geographical  background.  Besides, 
we  are  able,  by  the  kind  of  characters  we  introduce,  to 
indicate  the  general  scope  of  our  Exposition.  We  may 

1  See  p.  136. 


160    EXPOSITION   AND   ILLUSTRATION  IN  TEACHING 

have  half  a  dozen  historical  manuals  all  of  the  same  size, 
yet  dealing  with  widely  different  fields  of  history.  We 
may  have  one  dealing  with  Ancient  History,  another 
with  The  History  of  the  United  States;  a  third  may 
be  An  Epitome  of  the  History  of  the  World,  while  a 
fourth  is  The  History  of  Partney  Parish.  We  have 
here  four  quite  different  powers,  and  while  a  certain 
number  of  events  are  common  to  two  or  more  of  the 
volumes,  the  importance  of  those  events  is  entirely 
different  in  the  various  volumes.  The  Renaissance 
might  be  treated  in  four  different  powers  at  different 
times,  with  the  same  advanced  class.  Under  the  70 
objective  we  might  treat  of  the  great  movement  that 
north  of  the  Alps  culminated  in  the  Reformation  and 
on  the  south  of  the  Alps  hi  Humanism.  The  200 
objective  would  give  scope  for  a  lesson  on  the  state- 
ment that  "Modern  History  begins  with  the  reign  of 
Henry  VII."  Under  the  500  objective  there  would 
be  enough  detail  to  work  out  The  Effect  of  the  Renais- 
sance on  the  Public  Schools  of  England.  "The 
Renaissance  is  epitomised  in  Erasmus"  would  be  a 
theme  that  could  be  satisfactorily  treated  only  under 
the  1000-power  object-glass. 

This  sliding  scale  of  focus  emphasises  the  relativity 
of  everything  that  can  be  said  on  the  subject  of  Expo- 
sition. There  is  a  natural  desire  for  a  standard  of 
some  sort  to  which  different  cases  may  be  referred. 
The  ordinary  thermometer  with  its  two  fixed  points 
of  departure  —  the  freezing  and  boiling  points  of  water 
—  rouses  our  envy  and  challenges  competition.  In 
attempting  to  set  up  two  points  as  a  basis  of  comparison 
in  Exposition  it  must  be  remembered  that  we  are  work- 
ing on  the  subjective  side,  and  that  therefore  the  points 


CONDITIONS  OF  PRESENTATION  161 

will  vary  with  each  individual  treated.  It  is  com- 
paratively easy  to  standardise  the  expositandum,  the 
matter  of  Exposition,  but  so  soon  as  we  enter  upon  the 
subjective  consideration  of  that  matter  we  must  be 
prepared  for  difficulties;  we  must  face  the  problem  of 
the  individual  mind. 

It  is  possible  to  obtain  two  points  that  are  fixed  for 
any  given  individual  at  a  given  time.  They  change  in 
the  course  of  the  pupil's  development,  and  they  do 
not  coincide  exactly  in  the  case  of  different  pupils  at 
approximately  the  same  stage  of  development.  But 
they  are  fairly  definite  within  the  experience  of  the  in- 
dividual, and  the  coincidence  with  corresponding  points 
in  pupils  of  the  same  standing  is  sufficiently  close  to 
give  the  points  a  certain  practical  value. 

The  first  may  be  called  the  Inference  Point.  It 
marks  the  stage  in  any  given  subject  at  which  the  pupil 
has  to  go  through  a  process  of  inference,  however  slight. 
Up  to  this  point  everything  in  that  subject  that  is 
presented  to  the  pupil  is  accepted  at  its  face  value. 
If  on  glancing  at  the  sky  a  man  remarks,  "I  see  it  is 
going  to  be  a  fine  day  to-morrow,  "he  is  dealing  with  a 
matter  that  is  below  his  Inference  Point.  No  doubt 
he  is  really  making  an  inference  and  not  merely  record- 
ing an  observation.  He  does  not  see  that  it  is  going  to 
be  a  fine  day,  but  from  what  he  sees  he  infers  that  the 
day  is  going  to  be  fine.  So  closely  related,  however, 
are  the  facts  observed  and  the  deduction  drawn  from 
them,  that  the  whole  process  is  practically  one.  When 
a  number  of  facts  and  deductions  from  facts  are  so 
welded  together  as  to  become  independent  organised 
groups,  the  mind  requires  merely  to  observe  them 
in  order  to  accept  them  as  wholes  without  criticism. 


162    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

Wherever  this  happens,  the  mind  in  question  is  working 
below  its  Inference  Point.  But  when  the  Inference 
Point  has  been  reached,  it  is  necessary  to  do  conscious 
work.  Ideas  have  to  be  compared  and  correlated, 
and  deliberate  deductions  drawn  from  previous  expe- 
rience. A  medical  student  at  a  clinical  examination  is 
working  well  above  his  Inference  Point.  The  case 
may  be  an  easy  one,  but  the  student  is  quite  aware  of 
the  processes  by  which  he  reaches  his  conclusions. 
A  mere  glance  at  the  patient  tells  the  examiner  all  that 
it  is  necessary  to  know.  The  few  perceptual  impres- 
sions that  act  on  the  examiner's  mind  call  up  at  once 
certain  groups  of  ideas  with  which  they  have  become 
in  his  mind  so  closely  associated  as  to  form  one  whole 
which  represents  the  disease  from  which  the  patient  is 
suffering.  Obviously  the  Inference  Point  in  a  given 
subject  which  the  student  is  studying  is  continually 
rising.  What  he  has  to  reason  out  painfully  at  the 
earlier  stages  becomes  a  part  of  his  being.  As  soon  as  a 
fact  becomes  faculty,  it  falls  below  the  Inference  Point. 
With  growing  experience  fact  after  fact  takes  its  place 
in  complexes  that  remain  below  this  point.  The  num- 
ber of  groups  of  ideas  that  may  be  accepted  at  their  face 
value  is  always  increasing. 

Botanists  tell  us  that  at  the  tip  of  each  twig  there  is 
what  they  call  "  the  growing  point."  The  plant  as  a 
whole  increases  by  the  multiplication  of  cells  according 
to  their  special  fashions,  by  budding,  fission,  gemmation, 
or  what  not.  But  in  whatever  way  they  multiply  they 
always  produce  cells  of  exactly  the  same  kind.  Sap 
cells  produce  sap  cells  and  no  other  kind,  bast  cells 
other  bast  cells,  wood  cells  other  wood  cells,  and  so  on 
all  round  —  except  at  the  growing  point.  There  the 


CONDITIONS  OF  PRESENTATION  163 

cells  are  undifferentiated  and  multiply  so  as  to  produce 
cells  that  are  fitted  to  become  at  need  sap  cells,  or  cam- 
bium cells,  or  bast  cells,  or  whatever  other  kind  the  plant 
stands  specially  in  need  of  at  the  tune.  The  range 
above  the  Inference  Point  corresponds  to  the  growing 
point  of  the  plant,  is  indeed  the  growing  point  of  the 
mind.  It  is  in  this  region  that  the  nurture  of  the  mind 
takes  place. 

It  would  seem  as  if  there  could  be  no  limit  to  the 
region  within  which  inference,  conscious  inference,  is 
exercised.  But  there  is  an  upper  limit  to  the  region 
of  Inference  when  the  matter  is  considered  from  the 
point  of  view  of  teaching  and  learning.  The  Infer- 
ence Point  marks  the  limit  of  paid-up  mental  capital. 
All  the  matter  that  lies  below  it  may  be  called  upon  at 
a  moment's  notice,  with  the  full  assurance  that  it  will 
come  at  once  and  behave  as  it  is  expected  to  behave. 
It  is  organised  almost  to  the  automatic  level.  Above 
the  Inference  Point  the  matter  on  which  the  mind  acts 
is  still  organised,  though  the  organisation  is  less  com- 
plete. In  certain  directions  the  organisation  is  more 
and  more  to  seek,  and  a  stage  finally  comes  at  which 
the  subject  cannot  be  said  to  be  organised  at  all.  When 
this  stage  has  been  reached  in  a  given  subject,  we  may 
be  said  to  have  attained  the  Gaping  Point.  It  indi- 
cates the  limit  of  organisation  of  the  mental  content. 
Up  to  this  point  everything  is  dealt  with  under  definite 
categories.  The  mind  is  prepared  to  manipulate  the 
matter  in  certain  definite  ways :  it  puts  certain  standard 
questions  and  knows  how  to  deal  with  the  answers. 
If,  however,  some  matter  is  presented  that  the  mind 
does  not  know  at  all  how  to  deal  with,  the  Gaping  Point 
has  been  reached.  All  that  the  mind  can  do  is  to  turn 


164    EXPOSITION  AND   ILLUSTRATION   IN  TEACHING 

over  this  new  matter  in  various  ways,  look  at  it  from 
this  point  and  from  that;  in  fact,  gape  at  it. 

A  mineralogist  has  a  new  substance  presented  to  him 
for  examination.  It  is  not  sufficiently  characteristic 
to  be  at  once  classified  by  inspection.  Accordingly 
it  rises  above  the  Inference  Point.  He  proceeds  to 
apply  this  test  and  that  according  to  his  system. 
He  observes  its  colour,  its  crystalline  form,  and  its  gen- 
eral texture.  He  strikes  it  with  his  hammer  to  hear 
how  it  rings.  He  breaks  off  a  piece  to  discover  its 
fracture.  He  pounds  a  small  portion  to  get  the  colour 
of  the  powder.  He  tests  its  hardness  compared  with 
his  standard  minerals.  Then  he  goes  to  his  laboratory 
and  discovers  its  specific  gravity,  its  chemical  compo- 
sition, its  reaction  to  heat,  electricity,  and  other  things. 
All  this  while  he  has  kept  on  asking  certain  definite 
questions.  He  knows  exactly  the  sort  of  information 
he  wants.  His  examination  has  been  guided  by  pre- 
vious experience,  and  therefore  admits  of  experiment. 
If  now,  in  consequence  of  his  investigations,  he  finds 
that  not  only  does  the  result  not  fit  into  any  system  of 
classification  with  which  he  is  acquainted,  but  that 
several  of  his  individual  results  contradict  each  other, 
he  has  come  very  near  the  Gaping  Point.  It  remains 
for  him  to  consult  his  books  and  his  friends.  If  as  the 
result  he  finds  that  the  mineral  remains  a  mystery,  he 
has  actually  reached  the  Gaping  Point;  for  not  only 
does  he  not  understand  the  mineral,  but  he  does  not 
know  how  to  go  about  discovering  its  meaning. 

Everyone  who  has  had  experience  in  working  riders 
in  geometry  has  had  experience  of  the  Gaping  Point. 
At  first  we  treat  the  problem  in  certain  definite  ways 
dictated  by  previous  experience.  This  proposition 


CONDITIONS  OF  PRESENTATION  165 

and  that  will  be  applied.  But  if  after  a  time  every- 
thing we  know  has  been  applied  in  vain,  all  that  can 
be  done  is  to  gape  at  the  problem,  and  wonder  whether 
anything  will  turn  up  to  suggest  new  lines  of  investi- 
gation. We  look  at  our  drawing  upside  down,  side- 
ways, obliquely,  any  way  that  may  enable  us  to  surprise 
the  hidden  meaning;  just  as  we  do  in  that  typical  case 
when  we  are  reduced  to  the  Gaping  Point  by  the  very 
bad  handwriting  of  a  friend. 

Like  the  Inference  Point  the  Gaping  Point  is  not 
stationary.  After  many  illegible  letters  from  our 
friend  we  begin  to  know  that  certain  tiny  scratches 
mean  the;  that  a  particular  wriggle  always  means  ing, 
another  wriggle  ation,  and  a  third  ly;  that  what  looks 
like  e  is  always  a;  and  that  of  is  always  omitted.  Out 
of  this  we  form  a  system  by  means  of  which  we  can  pro- 
ceed scientifically  to  deal  with  the  body  of  the  letter, 
though  probably  at  the  end  there  will  be  a  small  por- 
tion still  left  at  the  Gaping  Point. 

But  if  it  is  important  to  remember  that  our  Inference 
and  Gaping  Points  are  continually  changing,  it  is  much 
more  important  to  realise  that  our  pupils'  Points  are 
quite  different  from  ours.  What  is  below  the  teacher's 
Inference  Point  is  often  at  the  pupils'  Gaping  Point. 
No  better  way  of  testing  a  teacher's  skill  in  manipulat- 
ing the  two  Points  could  be  found  than  an  examination 
of  the  use  he  makes  of  the  word  therefore.  With  mat- 
ter below  the  Inference  Point  of  his  pupils  the  teacher 
is  entitled  to  bring  his  therefores  closely  together,  but  in 
subjects  within  the  pupils'  Inference  zone  the  teacher 
should  see  that  a  good  deal  of  matter  is  placed  between 
each  therefore.  We  have  all  met  the  brilliant  mathe- 
matician who  puts  down  one  line  of  algebraic  symbols 


166    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

on  the  board,  immediately  followed  by  another,  the 
only  bridge  from  the  one  to  the  other  being  this  ag- 
gravating word.  Sometimes  it  takes  pages  of  close 
"figuring out"  before  a  pupil  contrives  to  bridge  the 
gulf  that  his  teacher  has  dismissed  with  a  therefore. 


CHAPTER  VII 

BEGINNINGS  IN  EXPOSITION 

ACCEPTING  the  view  that  Exposition  consists  essen- 
tially in  producing  among  the  elements  of  the  mental 
content  of  the  pupil  a  combination  that  coincides  with 
the  combination  existing  in  the  mind  of  the  teacher, 
it  is  obvious  that  there  must  be  a  double  process  of 
analysis  before  a  beginning  can  be  made.  First  the 
teacher  must  review  his  own  mental  content  so  as  to 
discover  which  elements  are  of  importance  for  the  pres- 
ent purpose.  Naturally  all  the  necessary  ideas  can- 
not be  called  up  at  once;  but  all  the  salient  elements 
will  readily  come  into  consciousness  and  the  presenta- 
tive  activity  of  all  the  other  relevant  ideas  will  be 
quickened  by  the  presence  in  consciousness  of  those 
that  have  actually  risen  above  the  threshold.  The 
subconsciousness  is  filled  with  ideas  bearing  upon  the 
subject.  The  mental  content  of  the  teacher  is  there- 
fore in  a  favourable  condition  for  entering  upon  the 
work  of  Exposition. 

Next  we  have  an  analysis,  as  far  as  this  is  possible, 
of  the  pupil's  mental  content  in  relation  to  the  matter 
about  to  be  presented  to  him.  This  process  obviously 
corresponds  to  the  beginning  of  the  Preparation  Step, 
dealt  with  in  our  last  chapter.  Before  we  can  prepare 
the  mind  of  the  pupil  we  must  discover  which  parts  of 
its  content  are  relevant  to  the  subject  in  hand.  The 

167 


168     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

regular  teacher  of  a  class  has  obviously  a  great  advan- 
tage in  this  particular.  From  his  previous  dealings  with 
the  pupils  he  has  a  very  effective  knowledge  of  the  ideas 
which  he  can  rely  upon  finding  at  their  disposal.  With 
a  new  subject,  or  an  entirely  new  branch  of  an  old  sub- 
ject, there  is  a  certain  danger  of  fogginess  about  the 
available  mental  content.  But  even  under  such  cir- 
cumstances the  class  teacher  need  seldom  wander  far 
afield  in  order  to  find  connecting  ideas.  A  teacher  with 
an  entirely  new  class  has,  of  course,  to  feel  his  way  by 
questions  and  careful  observation  of  the  effects  of  what- 
ever presentations  he  ventures  to  make. 

With  a  fairly  distinct  knowledge  of  the  ideas  to  be 
conveyed  to  the  minds  of  the  pupils  and  the  com- 
plexes to  be  formed  in  those  minds,  and  a  less  clear  but 
still  adequate  knowledge  of  the  ideas  and  complexes 
at  present  existing  in  the  minds  of  the  pupils,  the  teacher 
is  prepared  to  enter  upon  the  next  stage,  which  consists 
in  comparing  the  pupil  mental  content  with  the  teacher 
mental  content,  and  selecting  a  starting-point  for  the 
exposition.  It  will  be  found  that  the  two  mental  con- 
tents overlap  each  other  to  some  extent.  There  may 
be  a  larger  or  a  smaller  common  segment,  but  in  every 
case  where  Exposition  is  possible  there  must  be  some 
elements  common  to  the  two  contents.  If  no  common 
element  can  be  found,  Exposition  is  out  of  the  question. 
Very  frequently  with  a  new  or  difficult  subject  the 
teacher  has  to  cast  about  for  a  little  before  he  finds  the 
overlap  that  is  necessary  to  secure  a  starting-point. 
Sometimes,  on  the  other  hand,  the  two  mental  contents 
coincide.  In  other  words  the  pupils  have  all  the  ele- 
ments necessary  for  the  full  understanding  of  the 
matter  in  hand,  though  these  elements  may  be  at  pres- 


BEGINNINGS  IN  EXPOSITION  169 

ent  so  arranged  as  to  give  a  different  result  from  that 
desired  by  the  teacher.  The  complexes  in  the  pupil- 
mind  may  be  all  wrong  as  tested  by  an  objective  stand- 
ard; as,  for  example,  in  the  first  two  stages  of  Herbert 
Spencer's  progress  towards  a  true  theory  of  the  colour 
of  shadows.1  In  such  cases  the  teacher's  business  is 
to  break  up  the  false  complex  by  Confrontation  and 
replace  it  by  a  better.  But  it  sometimes  happens  that 
the  pupil's  complex  is  true  so  far  as  it  goes,  or  true  in 
certain  connections,  and  yet  there  are  other  com- 
plexes to  be  made  that  are  equally  true,  or  that  are 
true  in  a  wider  sense.  In  cases  of  this  kind  it  is  not 
necessary  to  break  up  the  first  complex.  It  may  be 
temporarily  analysed  in  order  to  separate  out  the  ele- 
ments so  that  they  may  be  built  up  into  the  new  com- 
plex that  for  some  reason  or  other  the  teacher  regards 
as  necessary  for  the  pupil.  But  there  is  no  need  to 
introduce  dispeace  into  the  original  combination  of 
ideas;  it  may  quite  well  coexist  along  with  the  new 
one,  as  a  permanent  part  of  the  pupil-content,  though 
the  elements  of  which  it  is  composed  may  now  be  cap- 
able of  forming  a  totally  different  whole  when  required. 
For  example,  the  complex  "primary  colours"  is  made 
up  of  the  elements  red,  blue,  and  yellow.  But  while 
this  is  found  to  be  a  true  collocation  so  far  as  pigments 
and  their  manipulation  are  concerned,  it  is  unsatisfac- 
tory when  colours  are  treated  from  the  standpoint  of 
psychology.  What  are  primary  colours  from  the  one 
point  of  view  are  not  primary  from  the  other.  But 
the  pupil  who  has  had  the  psychological  primary  colours 
—  red,  violet,  and  green  2  —  firmly  grouped  together 

1  See  p.  76. 

2  Cf.  A  Primer  of  Art,  by  the  Hon.  John  Collier,  p.  44. 


170    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

as  the  result  of  later  exposition,  need  not  dispense  with 
his  old  pigment  combination  of  red,  blue,  and  yellow. 
Both  complexes  are  useful,  each  in  its  place.  As  a 
matter  of  fact,  for  the  ordinary  needs  of  life,  we  have  to 
adopt  still  a  third  complex,  for  we  have  even  psycho- 
logical authority  for  the  statement  that:  "The  pri- 
mary colours  for  the  mind  are  the  four  principal  colours 
—  red,  yellow,  green,  and  blue."  1  When  we  begin  to 
study  chemistry  and  form  new  combinations  of  ideas, 
these  need  not  in  any  way  interfere  with  our  old  com- 
binations as  represented  by  such  familiar  phrases  as 
"acid  drops,"  or  "table  salt."  The  chemist  may  call 
these  "trivial  or  irregular  names,"2  but  they  represent 
wholes  that  are  as  real  as  those  represented  by  his 
systematic  terms.  The  rainbow  complexes  found  in 
Genesis  and  in  lyrical  poetry  need  not  be  broken  up 
because  we  have  formed  new  combinations  under  the 
heading  "the  refraction  of  light." 

It  is  seldom  that  the  teacher  needs  to  use  up  every 
individual  element  in  a  given  complex  in  order  to  build 
up  another  complex.  The  much  more  common  case 
is  that  there  has  to  be  a  general  analysis  of  the  pupil- 
content  in  order  to  get  the  elements  necessary  to  build 
up  a  desired  complex.  In  the  process,  it  frequently 
occurs  that  certain  elements  necessary  for  our  new  com- 
plex are  found  to  be  lacking,  and  must  be  supplied  by 
the  teacher  before  any  progress  can  be  looked  for. 
In  any  case  the  beginning  must  be  made  in  that  part 
that  is  common  to  the  pupil-content  and  the  teacher- 
content.  Frequently  there  are  many  possible  starting- 
points  within  the  common  area,  and  the  selection  must 

1  Lightner  Witmer :  Analytical  Psychology,  p.  181. 

1  Dr.  Edward  Frankland :  Lecture  Notes  for  Chemical  Students,  p.  11. 


BEGINNINGS  IN  EXPOSITION  171 

be  determined  by  the  purpose  the  teacher  has  in  view, 
and  the  line  he  intends  to  follow. 

While  it  is  admitted  that  the  teacher  must,  at  the 
beginning  of  his  exposition,  know  definitely  what  his 
purpose  is,  it  does  not  necessarily  follow  that  this  pur- 
pose need  be  communicated  to  the  pupil.  As  a  matter 
of  fact  at  present  serious  consideration  is  given  to  this 
problem  among  the  German  teachers.  There  is  much 
that  is  of  interest  in  the  discussions  that  centre  in  what 
they  call  the  Zielangabe;  that  is,  the  giving  or  state- 
ment of  the  purpose  of  the  lesson  at  the  very  start. 
The  term  is  usually  closely  associated  with  the  name 
of  Tusikon  Ziller,1  though  his  critics  spend  a  good  deal 
of  time  in  proving  that  the  idea  of  stating  clearly  at 
the  beginning  of  a  lesson  the  purpose  of  that  lesson  is 
none  of  his  invention,2  and  is  in  fact  of  very  venerable 
antiquity.  The  text  of  a  sermon,  the  title  of  a  book, 
the  heading  of  a  chapter  are  referred  to  as  familiar  ex- 
amples of  the  Zielangabe  in  ordinary  life.  But  such 
cases  do  not  always  supply  a  parallel.  Frequently 
the  text  and  the  title  are  used  to  whet  curiosity  rather 
than  to  indicate  purpose.  Indeed  the  misleadingness 
of  titles  is  a  cause  of  increasing  complaint  among 
readers.  When  the  student  of  elocution  punctiliously 
begins  his  recitation  with  " Barbara  Frietchie,  a  poem: 
by  John  Greenleaf  Whittier,"  his  introduction  can 
hardly  be  classed  as  an  example  of  the  Zielangabe. 

1  See  his  Allgemeine  Padagogik,  dritte  Auflage,  p.  162  ff. 

2  While  there  is  little  difficulty  in  finding  examples  of  the  applica- 
tion of  the  principle  of  the  Zielangabe,  it  is  not  so  easy  to  give  cases 
in  which  it  is  deliberately  applied  as  an  educational  principle.     As 
far  back  as  1780,  however,  we  find  E.  Ch.  Trapp  using  in  his  Versuch 
einer  Padagogik  (p.  315)  the  term  Zielsetzung,  which  he  uses  in  quite 
the  Zillerian  sense.     This  reference  I  found  in  Karl  Richter. 


172    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

But  when  in  our  peculiar  idiom  a  lecturer  tells  us  that 
he  "proposes"  to  do  certain  things  in  the  hour  at  his 
disposal,  we  have  a  genuine  Zielangabe. 

The  very  fact  that  writers  on  Education  have  thought 
it  worth  while  to  use  the  word  as  a  technical  term,  and 
to  discuss  its  exact  meaning  and  function,  marks  it 
out  as  indicating  a  noteworthy  stage  in  the  develop- 
ment of  the  theory  of  presentation.  It  indicates  among 
other  things  the  more  or  less  conscious  adoption  of  the 
heuristic  attitude  in  opposition  to  the  Socratic,  as  most 
suitable  for  the  teacher  to  take  up.  By  the  very  fact 
of  recognising  the  necessity  for  the  pupil  to  know  the 
object  of  the  lesson,  the  teacher  proclaims  that  he  ex- 
pects his  cooperation;  in  other  words,  the  activity  of 
the  pupil  is  assumed.  He  is  not  merely  to  be  supplied 
with  facts  and  conclusions;  he  is  to  be  made  to  work 
out  conclusions  for  himself.  The  goal  of  the  lesson  is 
set  before  him  as  something  to  be  attained;  the  means 
of  attaining  it  are  not  specifically  indicated.  A  great 
part  of  the  value  of  the  lesson  would  be  lost  if  this  were 
not  so.  Misapplications  of  the  heuristic  method  supply 
illustrations  of  the  abuse  of  the  Zielangabe.  "To  dis- 
cover the  chemical  composition  of  water"  is  a  legiti- 
mate Ziel  or  aim  to  set  before  a  class ;  but  when 
we  find  in  a  pupil's  note  book  that  the  matter  is  put : 
"To  find  the  chemical  composition  of  H20,"  we  realise 
that  something  has  gone  wrong.  On  the  other  hand: 
"To  prove  that  water  is  composed  of  Oxygen  and  Hy- 
drogen" is  quite  a  legitimate  Ziel. 

It  is  clear  that  the  Zielangabe  cannot  be  limited  to  the 
lesson-unit.  It  would  be  inconsistent  to  maintain  that 
the  pupil  must  know  definitely  the  purpose  of  each 
lesson,  and  yet  be  kept  in  ignorance  of  the  purpose  of 


BEGINNINGS  IN   EXPOSITION  173 

each  part  of  the  lesson.  One  Ziel  is  not  enough  to  guide 
throughout  a  whole  lesson.  There  must  be  many  inter- 
aims,  or  as  Campe  calls  them,  Zwischenziele.1  But  if 
there  are  to  be  inter-aims,  there  must  be  inter-units. 
We  must  have  our  matter  cut  up  into  sections,  at  the 
beginning  of  each  of  which  must  appear  an  inter-aim 
or  Zwischenziel.  Each  of  these  sections  must  be  com- 
plete in  itself,  the  completeness  being  determined  in 
relation  to  purpose.  They  need  not  by  any  means  be 
of  the  same  length;  the  one  condition  is  that  they  must 
be  little  wholes.2 

Sometimes  the  Zielangabe  becomes  a  mere  matter  of 
pedagogic  routine,  and  exercises  no  real  influence  on  the 
lesson.  This  is  specially  true  of  lessons  that  form  part 
of  a  course.  Here  the  whole  matter  dealt  with  by  the 
teacher  is  so  closely  connected  together  that  it  is  some- 
times neither  possible  nor  desirable  to  cut  it  up  even 
into  lesson-lengths,  not  to  speak  of  smaller  sections. 
The  general  amount  of  work  to  be  done  at  each  class 
meeting  must,  of  course,  be  determined,  but  it  does  not 
follow  that  the  whole  need  be  separated  into  purpose 
units  of  uniform  magnitude.  The  purpose  of  one  les- 
son has  frequently  to  be  carried  over  into  the  next. 
Accordingly,  we  find  that  sometimes  the  German  teacher 
who  is  loyal  to  the  theory  of  the  Zielangabe  finds  him- 

1  "  Soil  die  Jugend  auf  demselben  nicht  ermtiden,  so  muss  man  ihn 
durch  viele  Zwischenziele  verkurzen  und  angenehm  machen.     Auch 
ohne  Rucksicht  auf  Erleichterung  fur  die  Jugend  hat  dieses  Zielsetzen 
einen  grossen  Nutzen."     (Campe:  A llgemeine  Revision  des  gesammten 
Schul-  und   Erziehungswesens,  8  Teil,  1787,  S.,  180  ff.)     Quoted  by 
Karl  Richter. 

2  Amongst  certain  "long-known  rules  of  teaching"  Diesterweg  in- 
cludes "Lass  das  Kind  kleine  Ganze  auffassen;    gieb  ihm  kleine 
Ganze." 


174     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

self  forced  to  begin  with  the  ludicrously  attenuated 
Ziel:  "Our  object  in  to-day's  lesson  is  to  see  what  hap- 
pens next."  1  What  leads  to  this  absurdity  is  the 
notion  that  the  Zielangabe  is  a  sort  of  pedagogic  rite 
to  be  gone  through  at  the  beginning  of  each  lesson- 
period.  The  theory  of  the  Zielangabe  does  not  demand 
that  the  tune-unit  and  the  purpose-unit  must  be  iden- 
tical. The  essential  point  is  that  the  pupil  should  know 
whither  he  is  going,  so  that  he  may  cooperate  with  the 
teacher,  and  do  his  fair  share  of  the  work.2 

It  is  true  that  there  may  be  occasions  when  it  is 
not  only  unnecessary  but  unprofitable  for  the  pupil 
to  be  told  the  exact  purpose  of  a  lesson.  In  many 
lessons  given  on  the  Socratic  Method,  for  example, 
the  very  essence  of  the  teaching  is  the  unexpectedness 
with  which  certain  conclusions  are  reached.  It  is 
well  that  the  pupil  should  not  know  that  the  purpose 

1  "  Ja  nach  einer  Bemerkung  in  den  '  Erlauterungen  zum  Jahrbuche 
von  1883,'  die  also  nach  Zillers  Tode  erschienen  sind,  hat  Ziller  spa- 
ter  selber  stillschweigend  zugelassen,  dass  das  Thema  z.  B.  fur  eine 
Geschichtsstunde  auch  so  formuliert  werden  konne :  '  Wir  wollen 
sehen,  wie  es  weiter  geht.'"  Karl  Richter:  Die  Herbart  ZiUerschen 
Formalen  Stufen,  p.  131. 

*  "  Nicht  nur  der  Lehrer  muss  wissen,  was  er  in  dieser  Stunde  er- 
reichen  will,  sondern  auch  die  Schuler  sollen  es  wissen,  dass  ein  be- 
stimmtes  Ziel  gesteckt  ist,  iiber  das  sie  am  Schlusse  der  Stunde 
mussen  Rechenschaft  geben  konnen.  Dadurch  wird  der  Gedanken- 
gang  konzentriert,  es  wird  das  Gefuhl  der  Erwartung  und  Spannung, 
die  Lust  und  Freude  zur  Losung  der  gestellten  Aufgabe  erregt.  Fehlt 
jenes  Ziel,  so  wird  der  Schuler  wie  ein  Blinder  mit  verbundenen  Augen 
vom  Lehrer  gefuhrt,  und  eine  eigene  Willensanstrengung  ist  un- 
moglich.  Die  Schuler  mussen  am  Schlusse  der  Stunde  eine  bestimmte 
Antwort  auf  die  Frage  geben  konnen :  Was  habt  ihr  heute  gelernt  ? 
Wovon  habe  ich  gesprochen  ?  Schlimm  ist  es  wenn  sie  keine  Ant- 
wort  geben  konnen,  oder  vielleicht  sagen :  Wir  haben  allerlei  gehabt." 
Ferdinand  Leutz :  Lehrbuch  der  Erziehung  und  des  Unterrichts,  4  Au- 
flage,  Zweiter  Teil,  p.  40. 


BEGINNINGS  IN  EXPOSITION  175 

of  the  lesson  is  to  make  him  aware  of  certain  gaps  in 
his  knowledge.  In  the  Socratic  Method  the  pupil  is 
working  towards  two  ends:  one  that  he  knows  he  is 
working  towards,  and  one  that  is  known  only  to  the 
teacher.  It  does  not  follow  that  pupil  and  teacher  are 
working  at  cross  purposes.  We  are  dealing  here  with 
the  educational  effects,  and  these  are  best  produced 
without  the  pupil's  conscious  cooperation.  His  coopera 
tion  is,  of  course,  essential,  but  the  teacher  loses  his 
position  of  advantage  as  an  external  influence  if  he 
explains  to  the  pupil  the  educational  effect  to  be  pro- 
duced, and  urges  him  to  assist  in  being  educated. 

Even  in  matters  of  mere  knowledge  it  may  sometimes 
be  an  advantage  to  omit  a  statement  of  the  Ziel.  It 
is  largely  a  matter  of  the  distribution  of  interest. 
When  the  Ziel  is  given,  the  interest  lies  in  the  means 
of  attaining  it;  when  it  is  withheld,  the  interest  lies 
in  the  process  itself,  particularly  in  relation  to  the 
suspense  as  to  what  it  is  going  to  lead  up  to.  This 
contrast  between  the  place  of  the  Zielangabe  in  the 
Heuristic  and  the  Socratic  Method  will,  if  carefully 
investigated,  lead  to  the  conclusion  that  the  real  dif- 
ference lies  in  the  magnitude  of  the  purpose  unit. 
No  teacher  would  suggest  that  his  pupils  should  be 
kept  entirely  in  the  dark  with  regard  to  the  purpose  of 
the  work  he  is  engaged  in.  The  question  always  is: 
How  wide  an  outlook  is  it  advisable  to  offer  them? 
With  advanced  pupils  *  we  can  give  much  wider  aims 
than  those  that  apply  to  each  lesson  as  it  comes  round. 
It  is  probable  that  teachers  are  too  easily  content  with 

1  Campe  tells  us:  "So  wie  die  Jugend  heranwachst,  kann  man 
die  Hauptziele  nach  Monaten,  Viertel-und  halben  Jahren  stecken." 
Allgemeine  Revision  as  above. 


176    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

the  mere  Zwischenziele :  it  is  certain  that  the  pupils 
are.  So  long  as  the  pupil  is  allowed  to  go  on  dealing 
with  each  step  as  an  independent  unit,  he  is  usually 
quite  content  to  work  away  without  looking  for  any 
wider  or  deeper  meaning.  Pisgah  views  are  not  to  his 
liking,  and  he  will  certainly  not  climb  the  mountain 
unless  under  pressure,  or  at  least  under  encourage- 
ment. One  of  the  redeeming  features  of  school  ex- 
aminations is  that  they  bring  into  occasional  promi- 
nence the  main  aims  (Hauptziele),  that  give  meaning 
to  the  Zwischenziele  with  which  the  pupil  is  too  apt  to 
be  content. 

Teachers  of  arithmetic  are  now  laying  great  stress  on 
the  need  for  clearly  imaged  ends  in  the  minds  of  the 
pupils  before  beginning  to  work  out  problems.  The 
pupil  must  not  be  left  merely  to  multiply  and  divide 
in  the  hope  that  somehow  the  answer  will  come  out. 
The  following  extract  gives  a  graphic  account  of  a  state 
of  mind  that  is  too  common  in  our  schools.  It  is 
taken  from  a  school  story  called  The  Rickerton  Medal, 
which  is  the  work  of  a  practical  teacher.  The  scene  is  a 
a  class  room  in  an  elementary  school.  Mr.  Leckie,  the 
teacher  of  the  class  (Standard  VI,  average  age  about 
13),  propounds  a  problem  in  arithmetic:  — 

"If  7  and  2  make  10,  what  will  12  and  6  make ?  " 

A  look  of  dismay  passed  over  the  seventy-odd  faces  as  this 
apparently  meaningless  question  was  read.  Everybody  knew  that 
7  and  2  didn't  make  10,  so  that  was  nonsense.  But  even  if  it  had 
been  sense,  what  was  the  use  of  it?  For  everybody  knew  that  12 
and  6  make  18  —  nobody  needed  the  help  of  7  and  2  to  find  that  out. 
Nobody  knew  exactly  how  to  treat  this  strange  problem. 

Fat  John  Thomson  from  the  foot  of  the  class  raised  his  hand, 
and  when  asked  what  he  wanted,  said :  — 

"  Please,  sir,  what  rule  is  it  ?  " 


BEGINNINGS  IN  EXPOSITION  177 

Mr.  Leckie  smiled  as  he  answered :  — 

"  You  must  find  out  for  yourself,  John ;  what  rule  do  you  think 
it  is,  now  ?  " 

But  John  had  nothing  to  say  to  such  foolishness.  "What's  the 
the  use  of  giving  a  fellow  a  count l  and  not  telling  him  the  rule  ?  "  — 
that's  what  John  thought.  But  as  it  was  a  heinous  sin  in  Standard 
VI  to  have  "nothing  on  your  slate,"  John  proceeded  to  put  down 
various  figures  and  dots,  and  then  went  on  to  divide  and  multiply 
them  time  about. 

He  first  multiplied  7  by  2  and  got  14.  Then,  dividing  by  10, 
he  got  1§.  But  he  didn't  like  the  look  of  this.  He  hated  fractions. 
Besides,  he  knew  from  bitter  experience  that  whenever  he  had  frac- 
tions in  his  answer  he  was  wrong. 

So  he  multiplied  14  by  10  this  time,  and  got  140,  which  certainly 
looked  much  better,  and  caused  less  trouble. 

He  thought  that  12  ought  to  come  out  of  140;  they  both  looked 
nice,  easy,  good-natured  numbers.  But  when  he  found  that  the 
answer  was  11  and  8  over,  he  knew  that  he  had  not  yet  hit  upon  the 
right  tack;  for  remainders  are  just  as  fatal  in  answers  as  fractions. 
At  least,  that  was  John's  experience. 

Accordingly,  he  rubbed  out  this  false  move  into  division,  and 
fell  back  upon  multiplication.  When  he  had  multiplied  140  by  12, 
he  found  the  answer  1680,  which  seemed  to  him  a  fine,  big,  sensible 
sort  of  answer. 

Then  he  began  to  wonder  whether  division  was  going  to  work  this 
time.  As  he  proceeded  to  divide  by  6,  his  eyes  gleamed  with  tri- 
umph. 

"Six  into  48,  8  an'  nothin'  over, — 2-8-0  an'  no  remainder. 
I've  got  it ! " 

Here  poor  John  fell  back  in  his  seat,  folded  his  arms,  and  waited 
patiently  till  his  less  fortunate  fellows  had  finished. 


James1  knew  from  the  "if"  at  the  beginning  of  the  question  that 
it  must  be  proportion ;  and  since  there  were  five  terms,  it  must  be 

1  Scotice :  any  kind  of  arithmetical  exercise  in  school  work. 

2  The  clever  boy  of  the  class. 

N 


178    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

compound  proportion.    That  was  all  plain  enough,  so  he  started, 
following  his  rule. 

" If  7  gives  10,  what  will  2  give  ?  —  less." 

Then  he  put  down 

7 :2:  :10: 

"Then  if  12  gives  10,  what  will  6  give?  —  again  less."  So  he 
put  down  this  time 

12:6 

Then  he  went  on  loyally  to  follow  his  rule :  multiplied  all  the 
second  and  third  terms  together,  and  duly  divided  by  the  product  of 
the  first  two  terms.  This  gave  the  very  unpromising  answer  If. 

He  did  not  at  all  see  how  12  and  6  could  make  If.  But  that 
wasn't  his  lookout.  Let  the  rule  see  to  that. 

The  problem  of  beginning  is  often  complicated  by 
the  fact  that  it  is  not  recognised  as  a  problem.  It 
seems  so  easy.  There  are  so  many  possible  beginnings 
that  it  would  appear  that  one  could  hardly  fail  to  hit 
upon  something  that  will  exactly  meet  the  case.  Some 
teachers,  in  fact,  deliberately  minimise  the  importance 
of  the  beginning.  Too  much  time  is  spent  over  con- 
siderations of  beginning,  they  maintain,  and  advise 
their  pupils  to  get  to  work  anyhow.  The  important 
thing,  they  say,  is  to  get  a  start.  It  does  not  matter 
how  you  begin,  so  long  as  you  get  begun.  There  is 
perhaps  a  certain  justification  for  all  this  impatience. 
An  experienced  editor,  in  engaging  a  brilliant  young 
man  to  assist  him  in  preparing  for  the  press  manu- 
scripts that  had  been  accepted  for  his  magazine,  gave 
this  advice:  "In  many  cases,  particularly  with  essays, 
you  will  find  it  a  good  plan  to  cut  out  the  first  paragraph. 
The  author  gets  down  to  business  in  the  second. 
You  will,  of  course,  be  prepared  to  have  all  the  authors 
complain  that  the  first  paragraph  is  the  best  in  the 
essay,  the  fact  being  that  they  have  given  so  much  time 


BEGINNINGS  IN  EXPOSITION  179 

and  care  to  the  beginning  that  they  have  lost  all  sense 
of  its  true  value."  What  the  editor  objected  to  here  is 
not  so  much  beginnings  as  " introductions."  No  one  is 
more  tired  of  formal  openings  than  the  experienced 
trainer  of  teachers.  He  of  all  men  is  fully  convinced 
that  introductions  are  excellent  things  to  omit.  But 
the  lesson  must  be  begun  all  the  same,  and  the  problem 
of  the  beginning  remains. 

It  may  not  be  a  logically  justifiable  statement  that 
there  are  many  degrees  of  beginning,  but  it  contains  a 
definite  meaning.  We  have  indeed  the  whole  range  from 
the  beginning  of  an  entirely  new  subject  to  the  begin- 
ning of  a  new  sentence.  There  is  a  certain  rhythm  hi 
teaching,  and  each  new  beat  in  this  rhythm  implies  a 
new  beginning.  Obviously,  the  longer  the  beat  the  more 
important  the  beginning.  It  is,  however,  only  at  the 
bigger  divisions  of  a  subject  that  any  serious  prob- 
lem arises.  At  the  subordinate  divisions  the  begin- 
ning is  practically  determined  by  what  has  gone  before. 
In  dealing  with  a  subject,  the  teacher  acquires  a  swing 
that  carries  him  on  over  all  the  smaller  breaks  in  con- 
tinuity. A  lesson  in  the  middle  of  a  course  has  to  a 
certain  extent  determined  its  own  beginning  with  regard 
at  least  to  matter,  and  often  with  regard  to  form  as  well, 
inasmuch  as  the  reaction  between  teacher  and  pupil 
throughout  the  course  has  led  to  the  development 
of  the  teacher-  and  pupil-content  in  such  a  way  as  to 
establish  a  more  or  less  inevitable  interaction  between 
them.  But  the  very  beginning  of  a  new  subject, 
and  especially  when  the  teacher  is  new  to  his  class, 
presents  a  very  different  problem.  It  involves  the 
breaking  in  somewhere  or  other  into  the  pupils'  circle 
of  thought,  and  it  is  often  of  material  consequence 


180    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

where  this  irruption  takes  place.  The  subject-matter 
may  be  approached  from  many  different  points,  and 
nothing  but  a  fair  knowledge  of  the  pupils'  mental 
content  can  determine  which  it  is  best  to  select. 

That  this  difficulty  in  beginning  is  not  an  imaginary 
one  originating  in  an  excess  of  refinement  in  method  is 
proved  by  the  trouble  often  experienced  in  ordinary 
life  when  we  set  about  explaining  anything  that  is  in  the 
least  complicated.  We  often  toss  about  for  a  while, 
seeking  the  most  suitable  starting-point.  Sometimes, 
indeed,  we  actually  put  our  difficulty  into  words,  and 
ask:  "  Well,  now,  where  shall  I  begin? "  And  it  is  to  be 
noticed  that  we  do  this  even  in  what  we  are  apt  to 
regard  as  the  simplest  case,  that  is,  in  the  telling  of  a 
story.  When  a  Frenchman  does  not  follow  a  confused 
story  as  it  is  being  told  to  him,  he  is  apt  to  say  to  the 
story-teller:  " Si  tu  voulois  commencer  par  le  commence- 
ment." The  reference  is  to  Anthony  Hamilton,1  the 
brilliant  Irish  writer  of  French  fairy  tales.  In  one 
of  Hamilton's  stories  Moulineau  the  giant  calls  upon 
the  ram  (who,  of  course,  is  one  of  the  speaking  kind) 
to  cheer  him  up  by  telling  some  pleasant  tale : — 

"The  ram,  after  having  meditated  for  a  little,  began  in  this  way :  — 

'After  the  wounds  of  the  white  fox,  the  Queen  had  not  failed  to 
pay  him  a  visit.' 

'Ram,  my  friend,'  said  the  giant,  interrupting  him,  'I  understand 
nothing  of  all  that.  If  you  would  begin  at  the  beginning,  you  would 
give  me  pleasure ;  for  all  those  tales  that  begin  in  the  middle  only 
confuse  the  imagination.' 

'Very  well,'  said  the  ram;  'I  consent,  against  the  custom,  to 
put  everything  in  its  place ;  accordingly  the  beginning  of  my  story 
[histoire]  will  stand  at  the  head  of  my  narrative  [rtcit].'" 

1  Died  1720. 


BEGINNINGS  IN  EXPOSITION  181 

Here  Moulineau  takes  it  for  granted  that  it  is  a  self- 
evident  proposition  that  we  should  always  begin  at 
what  he  calls  the  beginning.  No  doubt  there  are 
intellects  for  which  this  rectilineal  arrangement  is  the 
best  possible.  Moulineau  would  have  been  at  home 
in  China,  where,  we  are  told,  the  drama  begins  with  the 
birth  of  the  hero,  and  goes  straight  on.  Even  in  Eng- 
land there  is  room  for  the  orthographic  story  of  the 
Robinson  Crusoe  type:  — 

"I  was  born  in  the  year  1632,  in  the  city  of  York,  of  a  good 
family,  though  not  of  that  country,  my  father  being  a  foreigner  of 
Bremen,  who  settled  first  at  Hull  .  .  ./'etc. 

but  there  is  also  a  place  for  the  Iliad,  Paradise  Lost,  and 
the  modern  complicated  novel  that  begins  in  the  middle 
of  the  plot.  Yet  Moulineau  is  right  in  insisting  upon 
beginning  at  the  beginning:  his  mistake  lies  in  suppos- 
ing that  chronology  is  the  only  element  that  determines 
what  a  beginning  is.  Time  is,  of  course,  of  fundamental 
importance  in  thinking,  but  it  must  not  be  allowed 
to  dominate  the  expositor  in  his  selection  of  material. 
He  must  be  guided  in  every  case  by  the  purpose  he  has 
in  view.  In  dealing  with  Moulineau  it  is  clear  that  the 
proper  order  is  chronological;  in  dealing  with  a  jaded 
public,  tired  of  the  ordinary  and  in  search  of  excitement, 
the  ram's  successors  are  entitled  to  neglect  the  chrono- 
logical order,  and  to  adopt  the  chronological  middle 
or  end  for  their  purposive  beginning.  The  expositor 
wishes  to  produce  a  certain  arrangement  of  ideas  in  the 
mind  of  another:  the  beginning  that  lends  itself  best 
to  the  production  of  this  arrangement  is  the  best. 

The  teacher  in  an  English  school  begins,  for  instance, 
with  a  blackboard  full  of  figures  from  the  Board  of 


182    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

Trade  returns  for  the  past  ten  years,  from  which  the 
pupils  are  invited  to  discover  which  are  Britain's 
best  customers  in  the  matter  of  buying  her  goods. 
Various  ups  and  downs  are  noticed,  and  causes  sug- 
gested. One  sudden  fall  is  unaccounted  for.  Tow- 
ards the  end  of  1906  Italy  began  to  buy  a  good  deal 
less  from  Britain.  The  fall  is  not  temporary,  for  there 
has  been  no  corresponding  rise  since.  Italy  is  not 
hostile  to  Britain:  rather  the  contrary.  The  cause 
must  be  sought  elsewhere.  More  figures  are  sub- 
mitted, from  which  it  appears  that  what  Britain  has 
lost  Germany  has  gained.  But  why  this  sudden  change  ? 
Germany  is  no  nearer  Italy  than  it  was  before;  there 
has  been  no  quarrel  with  British  goods;  the  Germans 
may  be  better  at  pushing  goods,  but  there  was  no 
sudden  increase  in  their  superiority  at  that  time. 
Gradually  the  search  is  narrowed  down  to  something 
peculiar  that  belonged  to  that  year,  and  the  opening 
of  the  Simplon  Tunnel  in  May,  1906,  is  suggested. 
Since  this  beginning  occurs  in  a  lesson  in  commercial 
geography,  the  tunnel  is  approached  from  the  proper 
point.  Moulineau  would  have  insisted  upon  start- 
ing with  the  tunnel. 

A  problem  of  this  kind  is  often  an  excellent  way  of 
beginning  an  exposition.  Instead  of  starting  straight- 
way with  the  subject  of  the  difference  between  the 
development  of  the  Feudal  System  in  England  and  in 
France,  the  problem  might  be  suggested :  Why  are  there 
hedgerows  in  England  and  not  in  France  ?  In  answer- 
ing this  interesting  question  all  the  essential  points  of 
difference  emerge,  and  the  incentive  of  a  well-defined 
purpose  is  maintained  throughout  the  lesson. 

The  problem  of  beginning  is  important  not  merely 


BEGINNINGS  IN  EXPOSITION  183 

because  of  its  relation  to  the  interest  aroused,  but  also 
because  it  practically  fixes  the  order  in  which  the 
lesson  must  afterwards  proceed.  In  a  lesson  on  the 
development  of  the  butterfly,  we  may  begin  with 
the  egg,  or  with  the  imago,  with  the  grub,  or  with 
the  chrysalis.  If  we  begin  with  the  egg,  we  would 
satisfy  Moulineau,  and  follow  the  development  up- 
wards. If  we  begin  with  the  imago,  we  follow  the 
development  backwards.  In  both  cases  we  have  no 
break  in  the  time  series.  If,  now,  the  start  is  made 
with  either  of  the  intermediate  states,  there  must  be  a 
double  progress,  one  part  forwards,  the  other  back- 
wards. At  first  sight  it  would  appear  that  there  is 
only  one  way  of  beginning  this  exposition  properly. 
The  egg  seems  the  only  natural  beginning.  But  most 
pupils  have  seen  a  butterfly,  while  comparatively  few 
have  seen  a  butterfly's  eggs.  In  most  cases,  though  the 
egg  would  form  a  part  of  the  teacher's  mental  content, 
it  would  not  form  a  part  of  the  pupil's,  and  therefore 
would  not  prove  a  suitable  commencing  element. 

On  the  other  hand,  if  the  teacher  possesses  specimens 
of  the  eggs  of  butterflies,  he  might  quite  well  start  with 
the  idea  of  egg  in  general,  which,  of  course,  forms  a  com- 
mon element  in  teacher-  and  pupil-content,  and  then 
present  the  specimen  eggs  as  new  matter  to  be  correlated 
with  the  old.  Out  of  the  common  elements  it  is  always 
the  teacher's  business  to  select  those  which  will  lead  to 
the  desired  result  with  the  minimum  expenditure  of  time 
and  energy.  In  certain  subjects  the  difficulty  of  choos- 
ing the  proper  elements  is  much  greater  than  in  others. 
In  mathematics,  for  example,  there  is  much  less  liberty 
of  choice  than  in,  say,  history  and  geography.  The 
connection  among  the  different  points  in  the  subject 


184    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

is  so  close  that  it  is  impossible  to  present  them  in  any 
but  one  order.  Yet  even  in  mathematics  there  is  great 
diversity  of  opinion  as  to  the  order  in  which  certain 
elements  should  be  presented.  At  what  stage,  for 
example,  should  the  idea  of  an  equation  be  introduced 
in  the  teaching  of  algebra  ?  Should  decimal  or  vulgar 
fractions  come  first  in  the  teaching  of  arithmetic? 
Again,  the  whole  of  the  propaganda  for  what  is  called 
the  new  geometry  is  an  exemplification  of  the  impor- 
tance placed  on  the  beginnings  as  determining  the 
after  processes. 

As  there  are  many  beginnings  throughout  the  course 
of  a  lesson,  so  there  are  many  endings.  Every 
beginning  implies  an  ending  of  the  same  degree  of  im- 
portance as  itself.  Naturally  the  ending  of  a  lesson  or  a 
section  has  to  be  as  carefully  considered  as  the  begin- 
ning. In  point  of  fact,  they  must  be  considered  together. 
Indeed  it  may  be  said  that  the  end  determines  the  begin- 
ning. The  principle  of  the  Zielangabe  demands  that 
the  pupil  shall  know  the  end,  at  least  in  the  sense  of  the 
aim  or  purpose.  But  the  teacher  must  know  the  end 
also  in  the  sense  of  the  termination.  He  must  know 
what  his  process  is  going  to  accomplish,  and  he  must 
also  know  how  his  process  is  to  terminate.  He  must 
know  the  end  from  the  beginning,  and  further,  he  must 
correlate  the  beginning  to  the  end.  It  is  true  that 
much  may  happen  of  a  very  unexpected  character 
between  the  beginning  and  the  end.  It  is  in  this  inter- 
mediate period  between  the  beginning  and  the  end 
that  the  teacher's  individuality  has  most  scope;  but  in 
order  that  he  may  make  the  best  use  of  his  opportunities, 
it  is  essential  that  at  the  preparation  stage  he  should 
determine  his  beginning  and  ending. 


BEGINNINGS  IN  EXPOSITION  185 

There  is  nothing  to  prevent  the  teacher  making  the 
beginning  that  he  fixes  upon  as  best.  The  plan  that 
he  resolves  upon  in  his  study  he  can  at  once  proceed 
to  carry  out  in  the  class  room.  With  the  ending  it  is 
different.  Too  frequently  the  actual  ending  has  little 
resemblance  to  the  ending  that  had  been  projected. 
Sometimes  in  the  course  of  a  lesson  the  teacher  dis- 
covers that  he  has  made  a  mistake  in  his  private  review 
before  the  lesson.  Occasionally  it  is  a  mistake  in  the 
subject-matter  that  he  did  not  notice  in  his  preparation, 
and  that  is  only  brought  out  in  the  process  of  teaching. 
More  usually  the  trouble  arises  from  the  discovery  that 
his  pupils  know  less  or  more  of  the  subject  than  he  had 
given  them  credit  for.  In  such  cases  it  is  essential 
that  the  predetermined  end  should  be  modified.  But 
in  all  other  cases  it  is  highly  desirable  that  the  selected 
end  should  be  reached.  The  teacher  must  be  very  elastic 
in  his  arrangements  for  meeting  unexpected  develop- 
ments in  the  course  of  the  lesson,  but  he  should  be 
tenacious  in  his  efforts  to  reach  the  predetermined 
stopping-place.  Unforeseen  difficulties  may  arise  to 
disturb  the  prearranged  distribution  of  time,  and  the 
teacher  may  thus  not  get  within  reasonable  distance  of 
the  point  at  which  he  had  resolved  to  close.  This  con- 
tingency should  be  provided  for  by  selecting  beforehand 
a  series  of  possible  endings  throughout  the  course  of  the 
lesson,  —  the  attainment  of  each  Zwischenziel  should 
be  a  possible  ending,  —  and  by  cultivating  a  very 
tender  conscience  with  regard  to  using  them.  The 
teacher  should  feel  that  every  time  he  has  to  adopt  one 
of  those  alternative  endings  he  has  made  a  blunder 
in  his  calculations.  On  the  other  hand,  to  persist 
doggedly  in  getting  to  a  prearranged  end,  whether 


186    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

the  pupils  are  able  to  follow  or  not,  is  worse  than 
a  blunder. 

In  any  case  the  point  at  which  the  lesson  actually 
stops  should  be  recognised  by  both  teacher  and  pupil 
as  a  natural  end.  It  must  not  be  a  mere  cessation  of  a 
process,  as  in  the  case  of  a  street  organ  that  stops  opera- 
tions in  the  middle  of  an  air.  Nor  must  the  teacher 
merely  allow  himself  to  run  down  like  a  clock  that  grad- 
ually ticks  more  and  more  feebly  till  at  last  it  stops. 
Nor  must  the  end  be  reached  by  mechanical  stages 
that  the  onlooker  can  anticipate.  The  mannerisms  by 
which  some  teachers  let  it  be  understood  that  the  end  is 
approaching,  frequently  indicate  rather  the  termina- 
tion of  the  hour  than  the  end  of  the  lesson.  The  true 
ending  is  felt  to  be  an  ending  as  soon  as  it  is  reached. 
At  the  end  of  a  discourse  it  used  to  be  the  custom  in 
France  for  the  speaker  to  add  the  words,  J'ai  Ait.  At 
the  end  of  an  address  arranged  in  the  admirable  form 
for  which  French  speakers  are  noted,  the  words  came 
as  the  inevitable  conclusion.  They  were  felt  to  be  the 
only  words  that  would  not  have  been  irrelevant  at  the 
point  at  which  they  were  introduced. 

In  every  case  the  ending  should  find  a  natural  place  in 
the  rhythm  of  interest.  The  predominant  feeling  at  the 
ending  points  should  be  one  of  satisfied  interest;  but 
this  satisfaction  should  be  unstable.  The  interest  in  the 
particular  section  should  be  exhausted,  but  the  interest 
in  the  wider  whole  of  which  the  section  is  a  part  should 
be  maintained.  The  interest  to  be  carried  forward 
should  belong  to  the  section  that  is  to  come,  not  to  that 
with  which  the  lesson  finished. 


CHAPTER  VIII 

ORDER  OF  PRESENTATION 

IT  is  one  thing  to  acquire  knowledge  for  oneself; 
it  is  quite  another  to  communicate  that  knowledge. 
When  we  say  we  have  mastered  a  subject,  we  mean  that 
we  have  not  only  amassed  all  the  available  matter, 
but  have  rearranged  that  matter  so  as  to  have  it  in  an 
organised  form,  in  which  each  element  occupies  its  true 
relation  to  all  the  others.  Teachers  are  apt  to  rest 
satisfied  when  they  have  reduced  their  mental  content 
to  this  logical  order,  and  to  think  that  they  have  nothing 
further  to  do  than  to  present  the  matter  in  the  order  to 
which  they  have  reduced  it.  Many  teachers  will  admit 
having  had  something  like  the  following  experience. 
When  preparing  for  the  first  time  a  scheme  for  a  sys- 
tematic course  in  a  certain  subject,  the  thought  forces 
itself  into  the  mind:  "Why  wasn't  I  taught  this  sub- 
ject in  this  logical  way  ?  When  I  was  a  pupil,  the  matter 
always  appeared  to  me  as  a  thing  of  shreds  and  patches  : 
I  shall  take  care  that  my  pupils  are  taught  differently." 
The  cause  of  the  trouble  is  that  we  are  confusing  know- 
ledge in  its  ripe  and  in  its  green  state.  The  logical  point 
of  view  necessarily  implies  a  complete  knowledge  of  the 
field  to  be  covered.  It  represents  the  view  that  we 
may  take  of  an  experience  that  we  have  had,  which  is 
never  quite  the  same  thing  as  the  anticipation  of  the 
experience  we  are  going  to  have.  The  learner  is  feeling 

187 


188    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

his  way  into  a  region  that  is  already  well  known  to  the 
teacher,  who  must,  therefore,  modify  his  presentation  to 
meet  the  needs  of  the  pupil  rather  than  to  satisfy  the 
demands  of  logical  sequence. 

It  is  natural  that  we  should  suppose  that  logic  ought 
to  determine  for  us  the  order  in  which  matter  should  be 
presented ;  but  experience  has  shown  teachers  that  they 
must  not  depend  too  much  on  logical  arrangement  in 
presenting  matter  to  young  people.  Even  when  dealing 
with  grown-up,  educated  people,  it  is  necessary  to  be  on 
our  guard  against  a  too  rigid  adherence  to  logical  pres- 
entation. In  describing  to  teachers  how  the  struc- 
ture of  animals  should  be  taught,  Sir  Archibald  Geikie 
interrupts  himself  to  remark :  — 

"  For  the  sake  of  logical  sequence,  I  have  placed  the  consideration 
of  form  before  that  of  function.  But  in  actual  practice  it  will 
not  be  always  possible,  even  were  it  desirable,  to  separate  these  two 
subjects  sharply  from  each  other. "  l 

It  may  be  logical  to  complete  an  account  of  the  struc- 
ture of  an  animal  before  saying  a  word  about  the 
functions  of  the  various  parts,  but  it  is  certainly  not 
the  best  mode  of  exposition.  The  head  of  a  London 
training  college,  in  dealing  with  grammar,  tells  us:  — 

"  Obviously  the  psychological  order  (and  that  is  the  order  to  be 
followed  in  school-teaching)  is  (1)  the  acquirement  of  the  use  of 
language ;  (2)  the  analytical  investigation  of  language  —  that  is, 
grammar.  But,  it  might  be  argued,  grammar  deals  with  the 
presuppositions  of  language,  and  therefore  the  logical  order  is 
(1)  grammar;  (2)  the  acquirement  of  language.  Teachers  have,  how- 
ever, discovered  as  the  result  of  much  unproductive  labour  that  it  is 
impossible  to  adopt  the  logical  order  in  teaching  children.  When, 
indeed,  the  pupil  has  reached  a  certain  stage  in  the  acquirement  of 

1  The  Teaching  of  Geography,  p.  109. 


ORDER  OF  PRESENTATION  189 

the  use  of  language,  then  grammar  may  be  a  means  of  helping  him  to 
increase  his  mastery ;  but  it  is  impossible  to  begin  that  way."  1 

Still,  it  must  not  be  supposed  that  even  in  dealing 
with  young  people  there  is  something  objectionable  in 
logical  sequence  in  itself.  On  the  contrary,  the  logical 
sequence  represents  the  ideal  order  which  must  be 
followed  as  far  as  that  is  possible.  Every  deviation 
is  a  concession  to  human  weakness.  For  the  teacher, 
the  logical  sequence  of  the  facts  to  be  dealt  with  is  the 
beginning  of  the  process  of  Exposition :  for  the  pupil,  it 
is  the  end. 

In  his  essay  on  the  Philosophy  of  Style,  Herbert  Spencer 
seeks  for  a  general  principle  underlying  all  the  recog- 
nised rules  for  verbal  expression,  and  finds  it  in  "the 
importance  of  economising  the  reader's  or  hearer's 
attention."  2  Every  time  we  use  the  wrong  word  or  the 
wrong  order  of  words,  we  cause  certain  wrong  combina- 
tions to  be  formed  in  the  mind  of  the  pupil,  and  the 
necessary  correction  of  these  errors  is  sheer  waste  of 
time  and  energy.  Spencer  does  not  go  into  the  mot 
propre  theory  that  for  a  given  place  in  a  given  sentence 
there  is  one  word,  and  one  word  only,  that  will  perfectly 
meet  the  case;  but  he  comes  near  to  maintaining  an 
equally  rigid  principle  for  the  order  of  words  in  a  sen- 
tence: "We  have  a  priori  reasons  for  believing  that  in 
every  sentence  there  is  some  one  order  of  words  more 
effective  than  any  other."  8 

Even  when  a  sentence  is  grammatically  correct  and 
is  ultimately  intelligible,  it  may  have  its  parts  so  badly 
arranged  that  an  altogether  disproportionate  amount 

1  L.  Brackenbury :  The  Teaching  of  Grammar,  p.  7. 

2  Essays,  Stereotyped  Edition,  Vol.  II,  p.  11. 

3  Ibid.,  p.  16. 


190    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

of  time  and  effort  must  be  expended  over  it.  Both  of 
the  following  sentences  by  English  authoresses  of  some 
distinction  exemplif y  bad  order  of  presentation :  — 

"  I  am  sure,  too,  the  reputed  Hibernian  has  afforded  much  inno- 
cent amusement  who,  on  making  his  first  journey,  asks  why,  if  it  be 
true  that  the  last  carriage  is,  as  he  has  been  told,  dangerous  to  travel 
in,  it  is  not  taken  off." 

"The  crowd  of  faces  congregated  round  her,  and  from  its  midst 
emerged  the  one  she  shunned  supremely ;  his  whose,  while  her  will 
remained,  she  must  with  the  last  remnant  of  it,  shut  away." 

It  is  probable  that  Spencer  carries  his  theory  into  too 
great  detail.  For  example,  he  prefers  the  English  order 
"black  horse"  to  the  French  " cheval  noir."  In  all 
probability  in  both  cases  the  two  words  are  simulta- 
neously received  by  the  mind,  and  the  figure  of  the 
animal  occurs  as  accurately  to  the  Frenchman  as  to  the 
Englishman.  For  it  has  to  be  noted  that  Spencer  in  his 
essay  takes  it  for  granted  that  all  thinking  is  figurative. 
His  view  is  that  if  we  mention  the  horse  first  we  at  once 
make  a  picture  of  it,  and  since  we  are  not  guided  as 
to  its  colour  we  are  more  likely  to  make  it  brown  than 
black,  because  there  are  more  brown  horses  than  black 
ones.  When  the  word  black  occurs,  we  have  to  recolour 
our  mental  horse,  and  in  this  way  lose  tune  and  waste 
energy. 

Spencer  should  have  gone  farther  with  his  contrast 
between  the  black  horse  and  the  cheval  noir,  for  the 
French  have  certain  very  definite  customs  in  the  matter 
of  the  order  of  their  adjectives.  The  underlying  prin- 
ciple appears  to  be  that  if  the  quality  is  inherent  in 
the  substantive,  the  adjective  should  precede;  while 
if  it  is  an  accidental  quality,  as  colour  or  nationality, 
it  should  follow.  "  Votre  aimable  fille  "  is  a  compliment 


ORDER  OF  PRESENTATION  191 

not  only  to  your  daughter  but  to  you  and  her  sisters. 
"Votrefille  aimable"  is  still  a  compliment  to  this  par- 
ticular daughter,  but  at  the  expense  of  her  sisters  and 
of  yourself  —  it  is  no  longer  taken  for  granted  that  ami- 
ability is  innate  in  your  family.  The  French  have  thus 
a  means  denied  to  us  of  conveying  a  distinction,  and  it 
is  not  likely  to  be  maintained  that  French  thinking 
is  retarded  in  consequence. 

Whatever  may  be  true  about  the  possibility  of  simul- 
taneously grasping  the  meaning  of  a  substantive  and 
its  adjectives,  there  can  be  no  doubt  that  when  we  come 
to  larger  divisions  of  thought  process,  great  differences 
occur  according  to  the  order  in  which  elements  are 
presented.  The  total  effect  of  a  presentation  is  not 
necessarily  the  same  in  two  exactly  similar  cases  be- 
cause precisely  the  same  elements  have  been  used  in 
each.  The  order  in  which  the  elements  have  been 
presented  counts  for  something,  frequently  for  a  great 
deal.  An  excellent  example  is  to  be  found  in  the  loss 
of  cumulative  effect  when  a  series  of  elements  is  pre- 
sented without  regard  to  their  degree  of  stimulating 
power.  A  passage  may  exemplify  the  rhetorical  figure 
of  climax,  or  may  convey  merely  an  unpleasant  effect  of 
mental  jolting,  according  as  the  elements  are  arranged 
in  regular  order  of  stimulus  or  "just  as  they  come." 

It  may  be  suggested  that  the  effect  here  is  rather 
aesthetic  than  intellectual,  and  it  may  be  asked:  Is  it 
not  possible  that  the  same  intellectual  effect  may  be 
secured  by  quite  different  orders  of  presentation  ? 
As  a  matter  of  fact,  it  may  be  urged,  we  have  practically 
all  of  us  gained  our  present  knowledge  and  opinions 
by  different  lines  of  study  and  experience.  No  two 
of  us  have  had  our  mental  content  presented  to  us  in 


192    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

quite  the  same  order.  This  has  to  be  admitted.  But  on 
the  other  hand,  it  will  hardly  be  denied  that,  however 
our  knowledge  has  been  acquired,  no  two  among  us  have 
quite  the  same  mental  content,  and  even  it  it  were 
possible  that  two  of  us  should  turn  out  to  have  the  same 
mental  content  so  far  as  matter  goes,  the  arrange- 
ment of  that  matter  would  be  almost  certainly  different. 
Mathematicians  are  usually  quite  willing  to  spare  a 
little  time  to  show  the  excessively  remote  chances  of 
mental  coincidences  of  this  kind.  We  are  what  we  are, 
not  merely  because  we  know  what  we  know,  but  because 
we  possess  our  knowledge  in  a  particular  way. 

It  is  true  that  even  if  we  have  been  badly  taught  we 
may  have  corrected  the  errors  into  which  we  have  fallen, 
and  have  now  reached  the  same  stage  as  others  who 
have  been  better  taught,  and  have  therefore  reached 
their  present  stage  with  less  difficulty.  But  it  is  at 
least  arguable  that  in  the  process  of  being  badly  taught 
the  pupil  has  received  permanent  injury,  as  well  as 
suffered  loss  of  time  and  energy.  It  may  be  that  our 
present  state  of  knowledge  in  any  subject  may  bear 
definite  traces  of  the  process  by  which  that  knowledge 
has  been  acquired.  In  one  of  his  Essays,  Grant  Allen 
tells  us  that  at  every  moment  we  are  shutting  out  one- 
half  of  the  possibilities  of  life,  that  every  choice  we  make 
is  a  dichotomy.  The  accompanying  diagram  may  re- 
present Grant  Allen's  view.  Starting  from  A  we  may 
reach  K  by  a  series  of  four  dichotomies.  We  may  ob- 
viously pass  from  A  to  K  in  various  ways.  We  may 
take  the  upper  passage  ABGHK,  or  the  lower  ACFEK; 
or  we  may  take  a  zigzag  course  ABDHK  or  ABDEK. 
The  important  point  for  us  to  consider  is  whether  the 
result  when  K  is  reached  is  the  same  in  all  cases,  nor 


ORDER  OF  PRESENTATION  193 

matter  what  the  route  has  been.  The  conclusion  seems 
inevitable  that  the  route  does  modify  the  result.  Take 
the  German  possessives  ihr  =  her,  and  sein  =  his.  To  a 


F 

FIG.  4. 

pupil  who  approaches  this  matter  from  the  standpoint 
of  English  there  need  never  be  any  confusion  between 
ihr  and  sein;  the  gender  of  the  substantive  possessed 
only  affects  the  words  to  the  extent  of  modifying  the 
termination.  To  an  English-speaking  pupil,  however, 
who  approaches  the  subject  through  French  there  is 
frequently  a  long  period  of  struggle  with  the  confusion 
that  results  from  the  fact  that  in  French  sa  may  mean 
his,  and  son  may  mean  her.  Experience  shows  that  in 
book-learned  German  this  confusion  persists  long  after 
a  clear  statement  of  the  facts  has  been  thoroughly 
understood  by  the  pupil.  He  has  an  intellectual  per- 
ception of  the  facts  of  the  case  quite  as  clear  as  that  of 
his  fellow  who  has  made  the  English  approach,  but  he 
does  not  know  them  in  quite  the  same  way. 
o 


194    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

The  very  adjective  used  above,  "book-learned,"  in 
itself  either  begs  the  question  or  proves  that  a  fact 
learned  from  a  book  is  not  quite  the  same  thing  as  the 
same  fact  learned  in  some  other  way.  The  balance 
certainly  appears  to  incline  towards  the  difference  of  the 
result  according  to  the  means  of  obtaining  it.  Pupils 
who  have  suffered  from  bad  exposition,  nearly  always 
retain  a  certain  lack  of  confidence  in  the  use  of  matter 
that  has  been  thus  presented  to  them.1  They  are  apt 
to  bring  in  as  part  of  the  completed  whole  certain  com- 
binations that  occurred  where  they  had  no  right  to 
occur  in  the  original  process  of  presentation.  They 
were  explained  away,  no  doubt,  at  a  later  stage,  but 
they  have  left  their  traces. 

Even  in  simple  narrative  the  order  of  presentation  is 
important  to  a  proper  understanding  of  the  point  to  be 
brought  out.  Here  the  mere  time  order  in  which  the 
events  occurred  is  usually  sufficient  to  determine  the 
order  of  presentation.  When  the  careless  story-teller 
breaks  in  upon  his  narrative  with  the  apologetic:  "Oh, 
by  the  by,  I  forgot  to  tell  you — "  it  means  that  he  has 
bungled  his  presentation.  It  does  not  as  a  rule  mean 
that  he  has  forgotten  some  unimportant  detail,  but  that 
he  has  suddenly  found  that  he  has  omitted  an  important 
section  without  which  the  whole  is  meaningless.  He 
has  accordingly  to  break  the  current  of  interest,  and 
generally  succeeds  in  confusing  the  impression  on  the 
listener's  mind.  This  does  not  mean  that  the  listener 
does  not  catch  the  point  of  the  story,  but  that  the  point 

1  The  ihr  and  sein  difficulty  may  entirely  disappear  under  the  in- 
fluence of  constant  use  of  German,  but  let  a  discussion  arise  about  a 
particular  case  and  the  old  doubt  will  sap  the  confidence  of  the  victim 
of  confused  presentation. 


ORDER  OF  PRESENTATION  195 

has  been  blunted.  In  order  to  illustrate  the  fact 
that  illiterate  people  may  form  a  just  estimate  of  the 
"values"  of  a  picture,  a  lecturer  told  the  story  of  the 
English  lady  who  was  accompanied  by  her  maid  while 
visiting  a  certain  Italian  church  in  which  there  was 
a  very  fine  picture  of  the  Flight  into  Egypt.  Talking 
down  to  the  intelligence  of  her  maid,  the  lady  asked  if 
she  did  not  greatly  admire  the  oleanders  in  the  picture. 
The  reply  contained  an  unintentional  reproof:  "I 
wasn't  thinkin'  o'  the  oleanders,  but  o'  the  'oly  family." 
Unfortunately  in  using  the  illustration  the  lecturer  began 
the  maid's  reply,  "I  wasn't  thinking  o'  the  'oly  family, 
but  -  Though  he  caught  himself  up  at  once  and 
reversed  the  order,  the  point  was  ruined.  No  amount  of 
emphatic  explanation  could  produce  the  clear-cut  effect 
the  illustration  had  produced  on  previous  occasions. 
The  audience  understood  the  point  all  right,  but  its 
effect  was  gone. 

The  general  line  of  presentation  is  practically  deter- 
mined by  the  beginning,  since  this  in  its  turn  is  deter- 
mined by  the  purpose  of  the  exposition,  as  was  shown 
in  the  last  chapter.  We  are  assumed,  therefore,  to 
know  (1)  the  purpose  we  have  in  view,  (2)  the  part  of 
the  pupil's  mental  content  that  is  relevant,  and  (3)  the 
new  material  we  propose  to  use.  The  question  now 
arises :  In  what  order  is  the  presentation  to  be  made  ? 
It  may  be  objected  that  it  is  hopeless  to  discuss  such 
a  question  apart  from  the  nature  of  the  particular 
matter,  as  this  would  seem  to  court  error  by  omitting 
the  most  important  element.  But  while  the  details  of 
presentation  must  always  be  determined  by  the  needs  of 
each  particular  case,  there  is  a  certain  body  of  general 
principles  that  are  applicable  to  all  cases,  and  give  us 


196    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

some  guidance  in  dealing  with  each  new  set  of  circum- 
stances. It  is  true  that  these  principles  are  of  a  some- 
what general  nature,  and  indeed  they  are  sometimes  so 
vague  as  to  amount  to  little  more  than  pious  aspirations. 
"Instruct  so  that  the  matter  given  shall  be  learned" 
does  not  seem  to  carry  us  very  far;  nor  does  it  greatly 
improve  matters  to  add  —  "  and  so  that  its  culture 
content  may  exercise  its  due  influence."  l 

But  certain  principles  that  bear  directly  on  the  order 
of  presentation  have  recommended  themselves  to 
teachers  generally,  and  have  obtained  very  wide  rec- 
ognition, perhaps  because  of  then*  very  obviousness. 
The  same  interest  in  presentation  that  led  Herbert 
Spencer  to  seek  for  the  underlying  principle  of  literary 
expression  induced  him  to  set  forth  in  his  little  book  on 
Education  2  those  fundamental  principles.  It  is  not 
suggested  that  he  originated  them,  and  it  is  not  our 
present  business  to  trace  each  of  them  to  its  source. 
We  are  mainly  interested  in  the  possibility  of  their 
application  in  our  work,  and  it  is  convenient  to  have 
them  in  the  clear  way  in  which  they  are  presented  by 
Spencer. 

There  are  six  of  these  principles  in  all,  but  only  the 
first  three  and  the  fifth  concern  us  here.  They  run: 
In  Education  we  should  proceed  (1)  from  the  simple  to 
the  complex,  (2)  from  the  definite  to  the  indefinite, 
(3)  from  the  concrete  to  the  abstract.  (4)  "  The  educa- 
tion of  the  child  must  accord,  both  in  mode  and  arrange- 
ment, with  the  education  of  mankind  considered  histori- 
cally." This  is  clearly  not  germane  to  our  present 
purpose;  but  from  it  is  drawn  a  principle  that  is  im- 

1  Otto  Wilmann:  Didaktik  als  Bildungslehre,  Band  II,  p.  64. 
J  Intellectual  Education,  Chap.  II. 


ORDER  OF  PRESENTATION  197 

portant  to  us.  As  a  special  case  of  this  fourth  principle 
comes  the  fifth.  (5)  We  must  proceed  from  the  empiri- 
cal to  the  rational.  (6)  "  Self  -development  should  be 
encouraged  to  the  uttermost "  is  now  very  generally 
accepted,  but  like  principle  number  four  it  has  no  direct 
bearing  upon  our  subject. 

In  the  very  severe  criticism  to  which  Spencer's  book 
on  Education  has  been  subjected,  it  is  interesting  to  find 
that  these  general  principles  have  met  with  the  least 
opposition.  They  have  not  indeed  escaped  altogether, 
but  most  of  the  objections  raised  are  concerned  with 
the  meaning  attached  to  certain  terms,  and  the  critics, 
after  they  have  made  their  protest,  practically  restate 
what  Spencer  wanted  to  say,1  though  his  mode  of  ex- 
pression did  not  quite  meet  with  their  approval.  For 
example,  we  are  left  a  little  in  doubt  whether  he  meant 
his  principles  to  be  principles  of  education,  or  merely 
principles  of  teaching.  As  a  matter  of  fact  he  lets  us 
understand  that  he  is  dealing  with  the  order  of  develop- 
ment of  the  mind,  and  since  Exposition  ought  to  follow 
that  order,  the  two  positions,  the  educational  and  the 
expository,  ought  in  his  opinion  to  coincide. 

It  will  be  generally  admitted  that  we  ought  to  pro- 

1  The  same  is  true  about  the  general  criticism  of  the  principles 
themselves,  apart  altogether  from  their  connection  with  Spencer. 
Their  blatant  obviousness  seems  to  urge  critics  to  find  fault  with  them. 
This  is  what  Tusikon  Ziller  has  to  say  in  his  Allgemeine  Padagogik: 
p.  262,  "...  und  so  falsch  der  Grundsatz  war,  das  im  Unterrichte 
vom  Einfachen  zum  Zusammengesetzen  fortzuschreiten  sei,  ebenso 
falsch  ist  der  andere  vulgare  Grundsatz,  dass  vom  Bekannten  zum 
Unbekannten  fortgeschritten  werden  musse."  Then  he  proceeds, 
as  one  expects,  to  explain  that  he  does  not  quite  mean  what  he  says. 
He  does  not  seek  to  reverse  the  principle,  but  merely  to  bring  out  what 
it  really  means.  We  advance  not  from  the  known  to  the  unknown, 
but  to  the  presently  unknown  "  mit  Hiilfe  des  Alten  und  Bekannten." 


198    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

ceed  from  the  simple  to  the  complex,  though  disputes 
naturally  arise  regarding  what  is  simple  and  what  com- 
plex. Spencer's  meaning  is  made  plain  in  his  own  words : 
"Not  only  that  we  should  proceed  from  the  simple  to  the 
combined  in  the  teaching  of  each  branch  of  knowledge ; 
but  that  we  should  do  the  like  with  knowledge  as  a 
whole."  *  Thus  stated,  the  principle  would  preclude 
the  exposition  of  a  complex  by  means  of  analysis; 
we  would  seem  to  be  limited  to  synthesis  in  our  teaching. 
But  it  may  readily  happen  that  the  pupil  knows  a  com- 
plex quite  well,  and  yet  is  ignorant  of  the  elements  of 
which  it  is  composed.  A  man  may  know  what  prose 
is  and  be  able  to  use  it  effectively,  without  knowing  the 
elements  of  which  it  is  composed  and  the  laws  of  their 
combination.  No  doubt  in  acquiring  the  mastery  of 
the  use  of  prose  the  man  followed  the  general  principle, 
but  in  Exposition  it  is  surely  legitimate  to  reverse  the 
process.  A  pupil  may  know  the  rule  for  dividing 
vulgar  fractions,  and  may  be  able  to  apply  it  with  great 
effect.  He  follows  his  instructions  to  "  invert  the  di- 
visor and  proceed  as  in  multiplication,"  and  gets  the 
desired  result.  He  knows  the  rule  as  a  complex,2  but  he 
may  not  be  aware  of  the  elements  out  of  which  the  rule 
is  built. 

In  such  a  case  the  expositor  may  well  proceed  from 
the  complex  to  the  simple.  There  is  sometimes  a  little 
confusion  between  the  simple  in  itself,  and  the  simple  to 
understand.  Spencer  is  aware  of  this  danger,  and  warns 

1  Education,  Chap.  II,  p.  65  (cheap  edition). 

*  Of  course  it  may  be  quite  reasonably  objected  that  a  well-taught 
boy  ought  not  to  have  this  complex ;  but  granted  that  the  pupil  has 
been  badly  taught)  the  expositor's  best  plan  is  to  work  from  the  re- 
sults already  attained,  however  bad  they  may  be. 


ORDER  OF  PRESENTATION  199 

teachers  that  "a  generalisation  is  simple  only  in  com- 
parison with  the  whole  mass  of  particular  truths  it  com- 
prehends— that  it  is  more  complex  than  any  one  of  these 
truths  taken  singly,"  1  and  thus  he  feels  the  necessity 
of  laying  down  the  "  concrete  to  abstract  principle." 
With  this  rule  the  teacher  need  have  no  quarrel,  since 
it  will  be  found  to  be  impossible  to  break  it.  It  is  true 
that  attempts  have  been  made  to  teach  in  the  reverse 
order,  and  to  pass  from  the  abstract  to  the  concrete. 
Indeed,  for  centuries  teachers  believed  that  they  were 
teaching  from  the  abstract  to  the  concrete.  They 
taught  Latin  by  laying  down  rules  and  then  setting  their 
pupils  to  apply  these  rules.  The  pupils  learnt  Latin, 
no  doubt,  but  not  because  of  the  rules  they  learnt.  They 
did  not  understand  Latin  because  of  the  rules,  but  the 
rules  because  of  the  Latin.  The  teachers  did  not  really 
teach  at  all.  What  they  did  was  to  provide  means  by 
which  Latin  might  be  learned,  and  then  to  place  their 
pupils  in  circumstances  in  which  it  was  unpleasant  not 
to  know  Latin.  The  master  thought  he  was  teaching 
from  the  abstract  to  the  concrete,  but  the  pupils  actu- 
ally learned  from  the  concrete  to  the  abstract.  It  is 
impossible  to  learn  in  any  other  way.  The  abstract  is 
necessarily  unintelligible  unless  it  has  been  reached  by 
means  of  the  concrete  from  which  it  has  been  derived. 
With  an  entirely  new  abstraction  in  relation  to  an 
entirely  new  bit  of  the  concrete  the  mind  can  work  in 
only  one  way.  The  concrete  must  precede.  But  in 
ordinary  experience  cases  of  pure  abstraction  are  rare. 
We  nearly  always  know  something  about  the  materials 
from  which  abstraction  has  been  made,  and  the  mind 
passes  from  what  it  knows  of  the  concrete  to  deal  with 

1  Education,  Chap.  II,  p.  67. 


200    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

the  abstraction  that  is  presented  to  it.  From  the  ab- 
stract statement  "Things  that  are  equal  to  the  same 
thing  are  equal  to  one  another"  the  pupil  may  be  made 
to  pass  to  the  concrete  case  that  if  Tom  is  the  same 
height  as  James,  and  William  is  the  same  height  as 
James,  then  Tom  is  the  same  height  as  William.  But 
the  abstract  statement,  so  far  from  making  clear  the 
equality  in  the  height  of  Tom  and  William,  would  not 
be  even  intelligible  to  the  pupil  but  for  many  similar 
measurements  that  have  been  made  in  his  experience 
before  the  abstract  statement  was  heard  of.  Indeed, 
is  it  not  a  contradiction  in  terms  to  maintain  that  one 
can  understand  an  abstraction  without  first  knowing 
the  something  from  which  the  abstraction  has  been 
made? 

The  truth  is  that  in  ordinary  life  there  is  a  constant 
alternation  between  the  abstract  and  the  concrete  in  the 
process  of  acquiring  knowledge.  By  careful  examina- 
tion of  the  concrete  we  reach  a  certain  abstraction; 
but  we  at  once  proceed  to  apply  this  abstraction  by 
making  a  new  connection  with  the  concrete.  As  the 
result  of  abstraction  from  many  concrete  cases  Mill 
enunciates  his  canons.  Forthwith  he  exemplifies  them 
by  means  first  of  letters,  and  then  by  still  more  material 
examples.  He  appears  to  be  teaching  from  the  ab- 
stract to  the  concrete,  but  in  so  far  as  his  abstractions  are 
understood  at  the  first  presentation,  they  are  under- 
stood in  terms  of  the  concrete  experience  of  the  pupil. 
Logical  presentation  is  possible  with  pupils  who  have  a 
wide  though  ill-arranged  knowledge  of  the  subject. 
Grammar,  for  example,  may  be  taught  in  logical  order  to 
a  person  who  has  a  really  good  working  acquaintance 
with  the  language  in  connection  with  which  it  is  to  be 


ORDER  OF  PRESENTATION  201 

taught.  The  very  limitation  here  involved  is  sugges- 
tive. The  language  assumed  to  be  known  forms  the 
necessary  concrete. 

In  many  cases  the  facts  to  be  presented  are  of  coordi- 
nate rank  and  may  be  brought  forward  in  almost  any 
order.  Take  the  different  kinds  of  subordinate  clauses 
as  these  are  dealt  with  in  the  analysis  of  sentences. 
It  does  not  matter  much  whether  we  begin  with  the 
Noun  Clause,  the  Adjective  Clause,  or  the  Adverb 
Clause,  on  the  understanding  that  the  pupils  have 
already  mastered  the  Parts  of  Speech  and  are  familiar 
with  their  functions.  On  the  other  hand,  if  gram- 
matical construction  is  being  approached  by  means  of 
the  Analysis  of  Sentences  instead  of  by  Parsing,  then 
it  might  be  desirable  to  begin  with  the  Noun  Clause 
rather  than  with  either  of  the  others.  Indeed,  when  the 
teacher  comes  to  the  point  of  choosing  the  order  of 
presentation,  he  will  almost  always  find  that  there  is 
some  one  order  that  for  some  reason  or  other  ought  to 
be  preferred.  Further,  this  order  is  not  a  permanent 
one.  Next  time  he  has  to  deal  with  the  same  matter, 
but  with  a  different  class,  he  may  find  that  a  different 
order  is  preferable.  The  different  clauses  of  Magna 
Charta  are  to  a  certain  extent  coordinate.  They  form 
part  of  the  one  great  document.  But  their  order  of 
presentation  would  be  different  under  different  circum- 
stances. For  example,  if  we  are  considering  the  docu- 
ment merely  as  a  document,  —  as  a  specimen  in  the 
science  known  as  Diplomatic,  —  the  clauses  would  be 
dealt  with  in  the  order  in  which  they  occur  on  the 
parchment.  In  general  constitutional  history  the  clauses 
would  be  presented  in  their  order  of  importance  to  the 
constitutional  history  of  the  country.  We  might  either 


202    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

begin  with  the  least  important  and  work  up  to  the 
most  important,  or  we  might  reverse  that  order.  On 
the  other  hand,  if  our  main  purpose  is  to  illustrate  some 
special  point  —  say  the  position  of  the  artisan  class 
hi  the  Thirteenth  Century  —  our  presentation  might 
centre  round  one  point,  say  the  term  Contenement.1 
If  our  interests  are  mainly  in  commercial  matters,  the 
clauses  dealing  with  weights  and  measures  and  personal 
freedom  of  movement  from  place  to  place  might  come 
hi  the  first  rank. 

It  not  infrequently  happens  that  in  expounding  a 
particular  subject  there  are  two  or  three  terms  to  be 
explained,  and  the  whole  subject  cannot  be  properly 
understood  until  these  subordinate  terms  are  made 
clear.  Sometimes  lengthy  expositions  of  these  sub- 
ordinate terms  are  given,  while  the  whole  process  of 
understanding  the  main  subject  is  suspended.  Occa- 
sionally this  is  inevitable.  But  we  must  regard  it  as  a 
danger  signal  when  we  have  to  introduce  some  such 
statement  as:  " Before  we  can  proceed  to  the  considera- 
tion of  the  subject  at  issue  it  is  necessary,  et  cetera, 
et  cetera."  Every  time  we  interpolate  explanatory 
matter  we  must  satisfy  ourselves  that  there  is  no  more 
suitable  place  for  it ;  and  when  we  see  no  way  of  avoiding 
the  interpolation,  we  must  do  all  we  can  to  prevent  its 
materially  interfering  with  the  flow  of  the  main  line  of 
thought. 

1  "  A  freeman  shall  not  be  amerced  for  a  small  fault,  but  after  the 
manner  of  his  fault;  and  for  a  great  crime  according  to  the  heinous- 
ness  of  it,  saving  to  him  his  contenement;  and  after  the  same  manner 
a  merchant,  saving  to  him  his  merchandise."  Then  the  explanation 
is  in  place:  Contenement  signifies  the  chattels  necessary  to  each  man's 
station,  as  the  arms  of  a  gentleman,  the  merchandise  of  a  trader,  the 
ploughs  and  waggons  of  a  peasant. 


ORDER  OF  PRESENTATION  203 

We  must  always  try  to  keep  our  subordinate  ex- 
planations closely  connected  with  our  main  subject, 
and  with  each  other.  In  order  to  explain  A,  of  which 
the  pupils  know  a  little,  we  may  have  to  explain  X  and 
Y,  of  which  they  know  less.  We  must  guard  ourselves 
against  leaving  A  and  Y  quite  isolated  while  we  plunge 
into  long  explanations  of  X.  We  must  adopt  at  least  a 
working  explanation  of  Y  while  we  are  elaborating  X, 
else  the  bearing  of  X  upon  A  will  probably  be  obscured. 
This  will  be  better  understood  by  an  example;  the 
writer  quoted  is  expounding  the  nature  of  Narrative :  — 


"A  narrative  is  a  representation  of  a  series  of  events.  This  is 
a  very  simple  definition;  and  only  two  words  of  it  can  possibly 
demand  elucidation.  These  words  are  series  and  event.  The  word 
event  will  be  explained  fully  in  a  later  section  of  this  chapter :  mean- 
while it  may  be  understood  loosely  as  synonymous  with  happening. 
Let  us  first  examine  the  exact  meaning  of  the  word  series. 

The  word  series  implies  much  more  than  the  word  succession: 
it  implies  a  relation  not  merely  chronological  but  also  logical ;  and 
the  logical  relation  it  implies  is  that  of  cause  and  effect.  .  .  ."  1 

Then  the  writer  goes  on  for  seven  pages  elaborating  the 
meaning  of  this  term  series,  before  he  begins  to  treat  of 
the  parallel  term.  But  thanks  to  his  thoughtfulness  in 
supplying  us  with  a  working  definition  of  event,  we  are 
able  all  the  time  we  are  considering  series  to  make  use  of 
both  this  term  and  the  term  event  to  help  us  in  under- 
standing what  the  expositor  is  telling  us  about  nar- 
rative. 

This  anticipatory  treatment  in  which  we  refer  to  cer- 
tain aspects  of  a  subject  before  we  actually  deal  with 
them  in  detail  is  applicable  on  a  large  scale.  In  plan- 
ning out  a  book,  for  example,  the  same  principles  obtain 

1  Clayton  Hamilton :   Materials  and  Methods  of  Fiction,  p.  44. 


204     EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

as  in  planning  out  a  chapter.  We  are  working  with  a 
different  size  of  unit,  but  the  principle  is  the  same.  This 
may  be  illustrated  by  reference  to  the  idea  of  unit 
itself  as  treated  in  this  book.  In  Chapter  II  we  have 
a  general  reference  to  the  idea  of  the  unit  of  Exposition, 
in  which  it  is  treated  in  connection  with  the  need  for 
destructive  process  in  preparation  for  constructive. 
Then  again  in  Chapter  IV  we  have  the  unit  regarded  as 
a  part  of  a  background,  where  we  have  to  deal  with  it 
at  the  stage  of  complexity  at  which  we  find  it.  Finally 
in  Chapter  XII  we  have  a  new  view  of  the  unit.  In  that 
chapter  it  is  used  for  purposes  of  comparison.  Instead 
of  being  something  to  be  analysed  out,  or  to  be  used  as  a 
brick  to  build  up  with,  it  is  to  be  used  as  a  standard 
by  which  quantities  of  all  kinds  may  be  measured.  It 
may  naturally  be  objected  that  it  is  bad  presentation 
to  separate  thus  the  different  aspects  of  the  same  sub- 
ject. Why,  it  may  be  asked,  does  not  the  writer  say 
all  he  has  to  say  about  the  unit  in  one  place,  and  have 
done  with  it?  But  it  is  all  a  matter  of  emphasis. 
If  in  planning  the  book  the  writer  had  determined  to 
lay  great  stress  on  the  notion  of  the  unit  as  such,  then 
he  would  have  devoted  a  chapter  to  this  subject,  and 
in  that  case  the  contents  of  some  of  the  other  chapters 
would  have  had  to  be  distributed  throughout  the  book, 
as  the  unit  has  been  under  the  present  arrangement. 
But  even  when  a  special  chapter  has  been  set  apart  for  a 
certain  subject,  it  sometimes  happens  that  an  aspect  of 
that  subject  is  better  treated  in  some  other  connection. 
Thus  though  there  is  a  chapter  (XIV)  on  the  Picture, 
this  is  limited  to  the  use  of  the  picture  as  illustration. 
In  Chapter  IV  some  pages  are  devoted  to  the  treatment 
of  the  picture,  but  here  it  is  the  mental  picture  that  is 


ORDER  OF  PRESENTATION  205 

under  discussion,  the  picture  the  pupil  forms  for  him- 
self as  the  result  of  verbal  description.  In  Chapter 
XIV  we  are  dealing  with  the  picture  as  something  ob- 
jective, in  Chapter  IV  as  something  subjective. 

The  index  of  any  book  one  takes  up  supplies  many 
illustrations  of  the  distribution  throughout  the  text  of 
the  treatment  of  certain  subjects  that  the  reader  might 
prefer  to  have  had  grouped  together  in  one  place.  But 
apart  from  the  fact  that  we  cannot  have  a  book  ar- 
ranged according  to  the  desires  of  each  reader,  it  has 
to  be  remembered  that  there  is  a  certain  compensating 
advantage  in  treating  the  same  matter  at  different 
stages,  and  in  different  connections.  There  is  an  ad- 
vantage in  familiarising  the  mind  of  the  reader  with  a 
given  fact  before  that  fact  is  brought  forward  for  more 
or  less  exhaustive  treatment.  Novelists  frequently 
introduce  a  fact  two  or  three  times  in  a  very  incidental 
way  at  the  early  part  of  the  story  in  order  that  it  may 
be  the  more  effectively  treated  when  its  turn  comes. 
This  principle  of  casual  introduction  of  matter  to  be 
afterwards  elaborated  may  be  used  by  the  teacher  in 
two  ways.  He  may  imitate  the  novelist  and  use  this 
order  of  presentation  in  order  to  build  up  interest. 
Several  illustrations  will  be  found  further  on  in  this 
chapter,  and  in  the  next  there  occurs  a  deferred  illustra- 
tion of  a  generalisation  from  Herbert  Spencer  quoted 
in  Chapter  III.  It  will  probably  be  felt  that  this  illus- 
tration is  not  only  useful  where  it  is,  but  that  it  has  an 
increased  force  in  relation  to  its  original  generalisation 
because  of  the  delay. 

[This  paragraph,  within  brackets,  is  deliberately  in- 
troduced in  order  to  explain  its  own  vices  in  relation  to 
the  principles  of  Presentation.  It  is  thrust  in,  you  will 


206    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

observe,  between  two  sections.  The  teacher  uses  a 
novelist's  device  in  two  ways:  one  of  them  has  been 
dealt  with,  the  other  is  yet  to  come,  and  this  paragraph 
is  thrust  in  between  them.  This  is  bad,  and  is  only 
justifiable  because  it  emphasises  a  defect  by  calling 
attention  to  it  at  the  very  moment  when  it  is  producing 
its  irritating  results.  The  paragraph  originates  really 
in  the  desire  to  call  immediate  attention  to  a  blunder 
in  presentation  that  has  just  been  made.  While  it  is 
excellent  to  refer  to  something  that  has  already  occurred 
in  a  book,  it  is  generally  a  mistake  to  refer  specifically 
to  what  has  not  yet  been  reached.  In  the  preceding 
paragraph  the  reader  is  practically  invited  to  turn  to 
the  next  chapter  and  read  a  particular  passage,  which 
he  is  then  to  compare  with  a  passage  in  Chapter  III. 
This  not  only  seriously  interferes  with  the  reader's  line 
of  thought  hi  this  chapter,  but  spoils  the  effect  of  the 
passage  he  is  invited  to  read.  That  passage  occurs 
in  a  certain  connection,  where  it  is  assumed  it  ought  to 
occur.  To  read  it  in  the  first  instance  apart  from  this 
connection  is  obviously  to  do  it  injustice.  It  is  quite 
different  hi  cases  where  we  are  ref erring  back  to  passages 
that  have  been  read  in  their  proper  order  and  are  now 
considered  in  a  new  connection.  The  same  objection 
does  not  lie  against  the  reference  in  the  previous  para- 
graph to  Chapter  XIV.  There  is  in  that  case  no  call  to 
turn  to  Chapter  XIV  at  all.  Its  very  title  conveys  all 
the  information  necessary  to  understand  the  reference 
in  the  text.  After  reading  in  typescript  the  above  de- 
plorable divagation,  my  colleague,  Dr.  T.  Percy  Nunn,1 

1  This  does  seem  a  most  inopportune  place,  but  in  the  absence 
of  a  preface  I  have  no  other;  —  I  want  to  express  my  indebtedness  to 
Dr.  Nunn  for  his  kindness  in  reading  through,  in  the  very  limited  time 


ORDER  OF  PRESENTATION  207 

so  far  from  helping  me  to  return  to  the  straight  path, 
led  me  into  temptation  by  sending  me  his  copy  of  a 
work  by  that  Master  of  Exposition,  Sir  Oliver  Lodge. 
I  looked  into  the  book  *  and  was  lost.  Sir  Oliver's  words 
in  the  Preface  form  an  admirable  commentary  on  what 
I  have  already  written :  — 

"Since  the  book  is  intended  to  be  useful  to  the  higher  class  of 
students,  it  seemed  very  permissable  to  adopt  a  method  which  I  al- 
ways use  in  teaching ;  viz.  to  begin  by  giving  some  ideas  at  first, 
and  to  gradually  polish  them  up  later,  rather  than  by  attempting  a 
too  highly  finished  statement  a&  initio  to  overburden  and  depress, 
and  possibly  to  confuse,  a  student.  Because  of  this  progressive 
arrangement,  I  may  be  permitted  to  urge  students  to  read  the  book 
through  before  proceeding  to  dip  into  it  by  help  of  the  index,  and 
before  taking  notice  of  references  forward  which  subsequently  it  is 
hoped  will  prove  useful."2  (Italics  mine,  to  emphasise  the  applica- 
tion to  the  present  book.) 

Naturally  the  same  principles  may  be  applied  in  oral 
Exposition,  but  with  a  greater  sense  of  responsibility,  as 
the  pupil  is  entirely  in  the  expositor's  hands.] 8 

The  second  use  the  teacher  may  make  of  the  inciden- 

just  before  going  to  press,  the  typoscript  of  this  book,  and  for  the 
really  valuable  criticism  and  help  he  gave. 

1  Modern  Views  of  Electricity. 

2  Those  who  are  interested  in  the  presentation  of  this  subject  will 
find  in  Modern  Views  of  Electricity  examples  of  "anticipations  "  and 
"references  forward"  on  pages  16,  17,  28,  42,  90,  94,  96,  98,  99,  105, 
128,  144,  etc.,  of  the  first  edition,  1889.    For  an  interesting  illustration 
of  the  preparation  for  a  subject  by  incidental  reference  to  it  in  order 
gradually  to  build  up  an  interest  in  it,  see  Sir  Oliver's  treatment  of 
the  topic  "Does  electricity  possess  inertia?"  in  sections  (not  pages) 
7,  42-48,  88,  89,  98,  105. 

3  On  re-reading  the  above  paragraph  illustrating  defective  arrange- 
ment it  strikes  me  that  I  have  rather  overdone  it.    We  could  hardly 
have  a  worse  case  of  congestion :  but  I  let  it  stand,  as  the  reader's 
irritation  will  only  emphasise  the  lesson  meant  to  be  conveyed. 


208    EXPOSITION   AND  ILLUSTRATION   IN   TEACHING 

tal  introduction  of  some  matter  before  it  is  really  wanted 
is  exactly  the  opposite  of  the  novelist's.  He  may  seek 
to  exhaust  the  intrinsic  interest  of  matter  that  is  to  be 
afterwards  used  as  illustration.  By  introducing  the 
attractive  matter  in  unimportant  places,  he  allows  the 
pupil  to  enjoy  its  interest  for  its  own  sake,  and  when 
this  has  been  repeated  two  or  three  times,  the  pupil 
is  ready  to  take  a  new  point  of  view  from  the  teacher, 
and  get  up  a  secondary  interest  at  the  proper  place.1 

Sometimes  the  order  of  presentation  is  determined  by 
very  practical  considerations.  In  preparing  hydrogen  it 
makes  some  difference  whether  the  pupil  is  told  to  pour 
in  the  water  before  he  is  told  to  pour  in  the  sulphuric 
acid.  In  that  form  of  practical  presentation  commonly 
known  as  "  directions, "  when  supplied  along  with 
machines,  implements,  or  commodities,  the  order  of 
presentation  is  of  vital  importance.  I  have  seen  the 
pointer  of  a  typewriting  machine  broken  because  the 
direction,  "Be  careful  to  lower  the  pointer  when  re- 
placing the  carriage"  occurred  after  the  instructions, 
"How to  replace  the  carriage."  At  the  head  of  every 
set  of  practical  directions  should  appear  the  caution: 
Please  read  the  directions  right  through  before  beginning  to 
,  etc. 

This  naturally  raises  the  question  of  the  help  that 
one  part  of  a  presentation  gives  to  another.  It  may 
happen  that  what  is  obscure  when  only  two  elements 
have  been  presented  becomes  quite  clear  so  soon  as  a 
third  element  is  brought  forward.  This  involves  the 
problem  of  suspended  understanding  during  a  process 
of  presentation.  Is  it  justifiable  to  present  at  a  given 
time  certain  matters  that  cannot  possibly  be  under- 

1  This  is  further  dealt  with  in  Chap.  XVI,  p.  391. 


ORDER  OF  PRESENTATION  209 

stood  by  the  pupils  till  at  a  later  stage  additional  matter 
is  supplied?  If  it  is  a  case  of  presenting  matter  that 
cannot  be  understood  at  all  at  a  particular  stage,  but 
must  be  got  up  by  memory  for  use  later  on,  it  will 
probably  be  agreed  that  the  presentation  should  not  be 
made.  It  is  different,  however,  when  the  presented 
matter  cannot  be  fully  understood  at  the  time  of  pre- 
sentation, but  will  be  fully  understood  when  additional 
matter  is  presented  at  a  later  stage.  Almost  all  our 
presentations  are  open  to  the  objection  that  the  matter 
brought  forward  cannot  at  the  moment  be  fully  under- 
stood. All  that  we  can  hope  for  is  that  it  may  not  be 
misunderstood.  From  the  material  supplied,  the  pupils 
may  make  premature  conceptions  that  must  after- 
wards be  painfully  destroyed  in  order  to  make  way  for 
the  correct  construction.  It  is  not  uncommon  to  hear 
post-graduate  students  who  are  being  trained  to  teach 
the  elementary  subjects  confess  that  they  never  under- 
stood the  true  meaning  of  what  is  called  simple  sub- 
traction till  they  saw  the  subject  taught  in  the  demon- 
stration school.  They  often  find  that  they  have  to 
break  down  and  reconstruct  all  their  idea  combinations 
on  the  subject.  So  with  pupils  who  have  been  taught 
scansion  or  music  on  purely  mathematical  lines:  there 
conies  a  period  of  necessary  reconstruction  when  they 
reach  the  stage  of  artistic  appreciation.  Pupils  who 
have  had  drawing  presented  to  them  as  a  system  of  fine- 
line  copying  from  the  flat  have  to  fight  very  hard  indeed 
before  they  can  break  up  the  false  combinations  and  by 
reconstruction  attain  the  freedom  to  use  drawing  as  a 
means  of  expression.  Doubtless  the  reader's  own  edu- 
cation furnishes  him  with  more  than  one  illustration 
of  this  need  for  reconstruction.  There  are  cases,  as  we 


210 

shall  see  later  in  the  chapter,  in  which  this  formation 
of  premature  conceptions  and  their  correction  may  be 
turned  to  good  account,  as  a  means  of  strengthening  a 
desired  aesthetic  or  moral  effect.  But  on  the  cognitive 
side  we  must  do  all  we  can  to  secure  the  correct  (not 
necessarily  the  complete)  conception  at  the  very  start. 

Taking  it  for  granted  that  certain  orders  of  presenta- 
tion are  more  economical  of  the  pupil's  time  and  energy 
than  are  others,  it  may  be  objected  that  the  teacher's 
business  is  not  to  save  the  pupil's  time  and  energy,  but 
rather  to  make  him  expend  both.  There  are  those  who 
maintain  that  the  best  progress  is  made  by  the  process 
of  trial  and  error.  The  argument  is  that  you  know  a 
thing  better  if  you  have  made  your  blunders,  and  found 
out  the  truth  for  yourself.  The  result  is  more  your  own 
than  if  it  had  been  pumped  into  you  by  a  watchful 
teacher  who  stood  by  all  the  time  to  prevent  the  possi- 
bility of  your  going  wrong. 

In  all  arguments  of  this  kind  there  is  a  slight  confu- 
sion of  thought  between  the  different  parts  of  a  teacher's 
work.  The  formation  of  character  is  one  thing,  the  ex- 
position of  a  subject  another.  A  man  may  often  be  a 
better,  because  a  stronger,  man  on  account  of  the  diffi- 
culties he  experienced  in  acquiring  the  knowledge  he 
needed.  But  it  does  not  follow  that  he  knows  his 
subject  better  because  he  had  to  study  it  under  bad 
conditions.  The  argument  of  those  who  underesti- 
mate the  value  of  careful  teaching  is  that  the  pupils 
become  emasculated,  and  unfit  for  any  serious  study. 
But  surely  it  is  idle  to  complain  that  we  are  doing  too 
much  for  our  pupils.  There  is  a  limit  beyond  which 
it  is  impossible  to  help  them  at  all.  Beyond  that 
limit  our  help  becomes  a  hindrance.  To  pass  that 


ORDER  OF  PRESENTATION  211 

limit  is  clearly  bad  Exposition,  but  up  to  that  limit 
the  more  we  can  help  the  pupil  the  better.  There 
always  will  remain  the  irreducible  surd  of  individual 
effort  that  cannot  be  eliminated  by  any  amount  of 
external  help. 

On  the  other  hand,  there  is  the  danger  that  some 
teachers  may  regard  the  giving  of  trouble  as  in  itself  a 
laudable  thing.  The  implied  argument  is  surely  easily 
disposed  of  by  a  reductio  ad  absurdum.  If  the  increasing 
of  the  difficulties  of  our  pupils  is  an  advantage,  it 
would  naturally  follow  that  the  worse  our  exposition 
the  better  for  our  pupils.  The  teacher  who  provided 
the  worst  text-books  and  made  his  pupils  work  under 
the  worst  conditions  would  do  them  most  good.  Some 
teachers  actually  adopt  this  attitude,  and  oppose  the  in- 
troduction of  the  metric  system  on  the  ground  that 
their  pupils  would  lose  the  enormous  advantage  of 
having  to  cope  with  those  curious  vestigial  items  5^  and 
30j  that  adorn  our  present  arithmetical  tables.  In 
the  course  of  a  recent  examination  in  Education  as  one 
of  the  subjects  for  a  university  degree,  I  set  the  follow- 
ing question :  — 

"  Speaking  of  the  limited  educational  curriculum  in  the  best  days 
of  Greece,  Professor  Bosanquet  asks :  '  How  was  so  much  made  out 
of  so  little  ? '  What  answer  would  you  suggest  ?  " 

A  large  percentage  of  the  candidates  took  occasion  to 
point  out  that  the  curriculum  was  not  nearly  so  inade- 
quate as  it  appeared.  The  subjects  studied  had  the 
advantage  of  several  difficulties  that  are  no  longer 
available  in  our  modern  schools.  For  example,  the 
Greek  characters  were  not  only  made  by  the  hand  and 
therefore  rather  clumsy,  but  they  were  arranged  with 


212    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

no  spaces  between  the  words,  and  to  separate  out  the 
individual  words  involved  a  great  exercise  of  attention 
and  ingenuity;  while  the  fact  that  the  Greek  numerals 
were  so  awkward  to  deal  with  provided  still  further 
opportunities  for  strenuous  training. 

The  truth  is  that  all  this  pother  about  the  dangers  of 
a  soft  pedagogy  is  based  upon  the  assumption  that  it  is 
possible  to  make  teaching  so  perfect  that  nothing  is 
left  for  the  pupils  to  do.  But  all  that  the  most  skilful 
presentation  can  do  is  to  prevent  the  pupils  from 
having  to  waste  their  time  in  unprofitable  ways  of 
expending  their  energy;  as,  for  example,  in  manipulating 
antique  tables  and  separating  words  that  should  never 
have  been  united.  The  better  the  exposition  the  more 
rapid  the  progress  of  the  pupils;  the  only  limit  to  their 
progress  under  these  conditions  being,  in  fact,  the  neces- 
sary limits  imposed  by  the  need  of  time  for  consoli- 
dation. 

For  it  has  to  be  remembered  that  a  pupil  cannot  go  on 
indefinitely  piling  up  knowledge,  no  matter  how  skil- 
fully it  may  be  presented.  However  brilliant  the  natu- 
ral parts  of  the  pupil,  and  however  skilful  the  expositor 
may  be,  there  is  a  limit  to  the  speed  at  which  a  pupil 
can  master  a  subject.  Even  the  plain  practical  man 
admits  this,  though  with  obvious  regret.  It  is  with 
reluctance  that  he  acknowledges  that  we  cannot  put 
old  heads  on  young  shoulders.  There  are  no  doubt 
sound  psycho-physical  reasons  why  even  an  Isaac 
Newton  requires  a  certain  minimum  of  years  before  he 
can  deal  with  certain  mathematical  problems.  For  our 
present  purpose  it  is  more  important  to  observe  that 
all  mental  processes  involve  a  certain  expenditure  of 
time.  Natural  processes  may  be  greatly  accelerated  in 


ORDER  OF  PRESENTATION  213 

a  forcing  house,  but  even  in  a  forcing  house  a  minimum 
time  limit  is  imposed.  Stupid  pupils  demand  a  long 
time,1  but  even  the  cleverest,  when  treated  under  the 
most  favourable  conditions,  must  have  a  minimum  tune 
to  consolidate  their  gains.  There  is  no  fear  of  excessive 
speed  through  excellent  exposition. 

The  figure  of  the  forcing  house  brings  forward  an- 
other aspect  of  the  objection  that  deserves  treatment, 
since  there  is  a  basis  of  truth  underlying  it.  Some 
writers  want  to  know  whether,  by  this  very  carefully 
prepared  exposition,  we  may  not  weaken  the  power 
of  initiative  of  our  pupils  and  make  them  incapable 
of  learning  anything  for  themselves.  It  is  pointed  out 
that  certain  schools  that  have  specially  laid  themselves 
out  to  prepare  pupils  for  examinations,  have  reduced 
the  art  of  Exposition  to  such  a  state  of  formal  perfection 
that  nothing  is  left  for  the  pupils  to  do.  But  cramming 
and  Exposition  are  different  things.  The  crammer's 
aim  is  to  get  his  pupil  to  reproduce  under  unhealthy 
conditions  a  certain  amount  of  information.  He  is 
not  concerned  how  the  matter  is  retained,  so  long  as  it 
is  there  when  called  for;  nor  whether  it  is  understood 
or  not,  so  long  as  it  can  be  put  down  on  paper  without 
betraying  any  lack  of  comprehension.  The  aim  of  the 
expositor,  on  the  other  hand,  is  frustrated  if  the  pupil 
does  not  understand  the  matter  presented.  But  surely 
the  more  easily  the  pupil  can  be  made  to  understand  the 

1  Experienced  coaches  have  great  faith  in  the  efficacy  of  time  in 
removing  difficulties.  Dr.  David  Rennet,  the  distinguished  mathe- 
matical coach  at  the  University  of  Aberdeen,  whose  success  in  pre- 
paring for  examinations  is  phenomenal,  is  sometimes  encouraging  to 
dull  but  earnest  pupils  when  they  are  worsted  by  a  problem  even 
after  it  has  been  explained.  His  remark  is :"  Aweel,  than.  Ye  must 
juist  wait  till  it  sipes  [soaks]  in." 


214    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

better.  It  does  not  follow  that  the  most  direct  recti- 
lineal exposition  is  the  easiest  in  the  long  run.  Every- 
thing has  to  be  judged  by  the  kind  of  understanding 
attained.  But  assuming  that  our  aim  is  the  highest 
form  of  understanding,  then  it  may  be  taken  for 
granted  that  the  easiest  way  to  attain  that  form  is  the 
best.  To  deny  this  is  to  assert  that  labour  and  trouble 
are  in  themselves  desirable.  If  there  is  any  suggestion 
about  "their  value  as  training, "  etc.,  it  is  a  sufficient 
reply  that  all  this  is  already  discounted  when  we  have 
accepted  as  our  aim  the  highest  form  of  result.  It  is  for 
this  reason  that  the  expositor  is  entitled  to  use  con- 
trast, and  even  contradiction,  if  he  can  show  that  these 
are  better  means  of  expounding  his  subject  than 
straightforward  presentation  of  facts  that  are  easily 
assimilated.  Under  certain  conditions  it  may  be  desir- 
able to  go  against  the  principle  of  economy  on  which 
Spencer  lays  so  much  stress.  But  in  all  such  cases  it 
will  be  found  that  we  are  keeping  to  the  spirit  of  Spen- 
cer's principle,  though  we  reject  the  letter.  It  is  well  to 
follow  the  line  of  least  resistance,  but  naturally  every- 
thing depends  upon  where  one  wishes  to  go.  The 
means  are  relative  to  the  end :  it  is  another  case  of  the 
longest  way  round  being  sometimes  the  shortest  way 
home. 

When  Nathan  led  the  unsuspecting  David  to  con- 
demn himself  in  the  person  of  the  robber  of  the  one 
ewe  lamb,  he  was  supplying  us  with  an  excellent  ex- 
ample of  a  "premature  conception"  that  had  to  be 
destroyed  and  reconstructed  before  the  prophet's  ex- 
position was  successful.  But  obviously  the  result  was 
worth  the  expenditure  of  time  and  energy.  Indeed,  it 
may  fairly  be  said  that  to  attain  the  result  the  prophet 


ORDER  OF  PRESENTATION  215 

had  in  view  the  roundabout  way  was  the  line  of 
least  resistance.  An  intellectual  understanding  of  the 
case  could  no  doubt  have  been  secured  in  David's 
mind  without  this  troublesome  reconstruction,  but  the 
prophet  wanted  something  more  than  mere  intellectual 
consent. 

In  Nathan's  case  the  matter  was  so  skilfully  pre- 
sented that  there  was  no  room  for  error.  The  recon- 
struction was  not  called  for  till  the  very  moment  it  was 
needed,  and  the  first  construction  did  not  in  itself  in 
any  way  conflict  with  the  effect  of  the  second.  But  the 
greatest  care  is  necessary  to  prevent  the  first  construc- 
tion from  making  the  second  impossible.  An  amiable 
old  gentleman  was  called  upon  to  propose  a  vote  of 
thanks  to  the  chairman  and  governors  of  a  great 
school  at  the  distribution  of  prizes.  Tired  of  the  con- 
ventional way  of  doing  what  was  expected  of  him,  he 
thought  he  would  introduce  an  agreeable  variety  by 
emphasising  the  brighter  side  of  a  governor's  office. 
Accordingly  he  pointed  out  that  though  the  duties  of  a 
governor  were  very  exacting,  and  involved  a  great 
expenditure  of  time  and  energy,  the  governors  were 
very  well  paid  for  it.  He  had  intended  to  round  off  his 
speech  with  a  glowing  account  of  the  joys  of  being  kept 
young  by  constant  contact  with  the  fresh  young  life 
that  he  saw  before  him,  and  of  being  cheered  by  the 
glow  of  good  work  well  done,  and  a  number  of  other 
compensating  satisfactions  that  come  by  way  of  re- 
ward to  the  conscientious  governor.  But  at  the  mere 
words  "well  paid  for  it"  there  arose  such  a  murmur 
of  protest  among  the  assembled  governors  that  the  re- 
mainder of  the  amiable  gentleman's  speech  consisted  of 
a  hurried  explanation  that  "that  is  not  what  I  meant." 


216    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

This  unhappy  gentleman  applied  unskilfully  an  arti- 
fice that  is  quite  legitimate  in  Exposition.  He  sought 
to  create  a  vacuum  for  a  fact  that  he  proposed  to  pre- 
sent. He  knew  that  his  remark  would  excite  a  certain 
amount  of  surprise  which  would  in  its  turn  lead  to  a 
curiosity  that  he  would  then  proceed  to  satisfy.  He 
had  not  calculated  on  surprise  passing  over  into  indigna- 
tion instead  of  into  curiosity.  With  the  less  personal 
issues  raised  in  instructing  in  school  it  is  often  desir- 
able to  apply  this  principle  of  the  vacuum.  If  the 
teacher  can  create  the  desire  for  a  particular  bit  of 
knowledge,  he  is  on  the  way  to  the  best  possible  pres- 
entation of  that  knowledge.  The  following  example 
from  actual  teaching  illustrates  what  is  meant.  It  is 
taken  from  the  essay  of  one  of  my  students  at  the 
University  of  London :  — 

"I  was  teaching  a  class  to  scan  the  hexameter  line  in  Latin,  and 
after  teaching  the  division  of  the  line  into  six  feet,  two  beats  in 
each  foot  made  by  either  dactyl  or  spondee,  and  the  invariable  na- 
ture of  the  fifth  and  sixth  feet,  I  put  up  some  lines  on  the  board  for 
us  to  work  out  together.  The  pupils  got  on  swimmingly  for  the 
first  line,  as  the  lengths  of  the  syllables  were  well  known  to  them. 
But  the  second  line  was :  — 

'  Mutat  terra  vices,  et  decrescentia  ripas.' 

Working  backwards,  they  arrived  at  all  the  feet  except  the  first, 
and  there  they  stopped  in  difficulty.  Only  two  syllables  were  left 
for  this  foot,  and  they  had  been  carefully  taught  that  the  third 
person  singular  present  indicative  of  the  four  conjugations  was  short. 

Was  the  foot  a  trochee w  ?    That  was  the  time  for  the  explanation 

of  'vowels  long  by  position,'  which  would  have  been  imperfectly 
comprehended  if  given  before  the  children  had  found  the  difficulty 
for  themselves." 

Leaving  to  specialists  the  decision  of  the  question 
whether  scansion  should  ever  be  taught  in  this  way. 


ORDER  OF  PRESENTATION  217 

whether  in  direct  or  in  inverted  order,  it  is  necessary  to 
point  out,  what  the  student  herself  discovered  after 
sending  in  the  essay,  that  the  application  of  the  vacuum 
here  involved  the  fallacy  of  assuming  that  the  pupils 
would  make  et  long  by  position  in  order  to  get  into 
difficulties  at  the  end  so  as  to  be  led  to  enquire  into 
the  very  rule  that  they  had  already  applied.  The 
student's  reply  was  that  her  plan  worked:  she  desired 
to  get  the  pupils  into  this  difficulty,  and  she  succeeded. 
Obviously  the  excellence  of  the  plan  is  not  diminished 
by  the  fact  that  a  more  suitable  verse l  was  not  chosen. 
The  principle  of  the  vacuum  may  be  usefully  applied 
in  the  introduction  of  new  technical  terms.  If  at  the 
beginning  of  teaching  geometry  we  speak  a  great  deal 
about  "  the  line  joining  the  opposite  angles  of  a  square," 
the  pupils  will  get  tired  of  the  cumbrous  phrase,  and 
when  the  term  diagonal  is  introduced,  will  welcome  it 
as  a  relief  from  the  wearisome  description.  In  science 
teaching,  the  principle  may  be  applied  by  giving  half  a 
dozen  applications  of  a  certain  rule,  e.g.  different  phe- 
nomena resulting  from  the  pressure  of  the  atmosphere, 
without  enunciating  the  rule  till  the  last  application  is 
made.  By  this  tune  the  pupils  want  to  know  what  is 
the  cause  of  the  peculiar  phenomena  they  have  seen, 
and  are  glad  to  have  such  an  economical  arrangement  as 
one  principle  (whether  given  by  the  teacher,  or,  better, 
discovered  by  themselves)  to  explain  half  a  dozen  re- 

1  The  verse  — 

"  Scindit  se  nubes,  et  in  sethera  purgat  apertum  " 

would  have  led  to  the  desired  result,  and  would  have  had  the  addi- 
tional advantage  of  including  a  third  person  singular  (purgat)  that 
follows  the  usual  rule,  and  therefore  emphasises  the  difference  in 
sdndit. 


218    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

markable  things  that  at  first  appear  altogether  different 
from  each  other. 

Sometimes  the  principle  is  more  deliberately  applied. 
A  certain  problem  is  stated,  and  various  more  or  less 
plausible  solutions  are  offered  one  after  the  other, 
and  each  dismissed  in  turn  as  unsatisfactory.  But  all 
through  the  discussion  there  is  constant  reference  to  the 
true  theory.  Phrases  like  the  following  are  scattered 
throughout:  "as  we  shall  see  presently";  "when  we 
come  to  what  we  hold  to  be  the  true  theory";  "as  will 
be  evident  in  the  light  of  the  theory  about  to  be  pre- 
sented;" "a  natural  mistake  in  a  writer  who  has  not 
the  information  that  is  about  to  be  laid  before  you." 
For  example,  the  lesson  may  be  on  those  curious  medal- 
lions that  the  antiquarians  of  the  seventeenth  and 
eighteenth  centuries  called  contorniates.  The  un- 
skilled would  naturally  regard  them  as  coins.  People 
who  know  more  are  aware  that  this  is  not  so,  and  various 
theories  as  to  their  nature  have  been  held,  such  as 

(1)  amulets  to  bring  success  to  competitors  at  the  games; 

(2)  tickets  to  reserved  seats  at  the  games;    (3)  lots  to 
determine   the   starting   order   in   the   chariot   races; 
(4)  medals  indicating  success  in  the  games.     Now  the 
teacher  starting  with  the  view  that  the  true  use  of 
contorniates  was  to  serve  as  "men"  in  certain  table 
games  resembling  our  "draughts,"  keeps  this  in  view 
all  the  time  he  is  discussing  the  other  theories,  and  takes 
every  opportunity  of  shadowing  it  forth  without  actu- 
ally stating  it.     While  pointing  out  all  the  difficulties  of 
the  other  theories,  he  refers  to  "  the  better-supported " 
theory,  "the  clue  is  to  be  found  in  M.  Froehener's 
brilliant  suggestion,"  *  "before  what  we  believe  to  be 

1  Annuaire  de  Numismatique,  1894,  p.  88  :  quoted  by  K.  A.  Mac- 
dowall,  in  the  Numismatic  Chronicle,  Fourth  Series,  Vol.  VI. 


ORDER  OF  PRESENTATION  219 

the  true  solution  was  offered."  By  the  time  the  Froe- 
hener  theory  is  actually  presented,  a  real  need  for  it  has 
been  created.  The  pupil  is  tired  of  indirect  suggestions, 
and  welcomes  the  positive  statement  of  the  final  theory. 

There  is  one  limitation  to  the  application  of  the  prin- 
ciple of  the  vacuum  in  Exposition.  The  pupil  should 
not  be  taught  anything  that  is  actually  false.  In  using 
contrast  and  in  preparing  a  vacuum,  error  is  introduced, 
no  doubt,  but  in  the  first  place  it  is  not  taught  as  truth, 
and  in  the  second  place,  the  error  is  only  relative.  It 
must  be  associated  with  a  certain  amount  of  truth 
before  it  can  have  any  value  in  a  process  that  seeks  to 
pass  from  apparent  truth  to  a  nearer  approach  to  ulti- 
mate truth.  There  has  to  be  reconstruction,  perhaps, 
but  the  original  construction  is  usually  correct  for  some 
other  set  of  circumstances,  though  unsuitable  for  the 
present.  There  can  be  no  justification  in  presenting 
matter  that  is,  so  far  as  we  know,  false  under  all  cir- 
Icumstances.  We  want  the  pupil  to  get  at  the  truth 
las  it  is  known  to  us,  and  though  we  may  find  it  desir- 
able to  contrast  his  view  of  truth  with  ours,  we  need 
never  present  actual  falsehood  to  him. 

We  must  distinguish  between  falsity  and  mere  in- 
completeness in  presentation.  "An  instrument  for 
telling  the  time"  is  an  incomplete,  but  not  a  false, 
definition  of  a  watch.  Many  teachers  are  willing  to  al- 
low an  incomplete  presentation  of  ordinary  terms,  but 
draw  the  line  when  technical  words  are  in  question. 
Dr.  T.  Percy  Nunn  is  frequently  challenged  by  his 
students  of  the  London  Day  Training  College  for  giving 
"wrong"  meanings  to  scientific  terms.  For  example, 
he  deliberately  calls  a  mass  of  peroxide  of  lead,  whatever 
its  size,  a  "molecule,"  and  when,  under  heat,  it  gives  up 


220    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

just  the  amount  of  oxygen  to  enable  it  to  become  lith- 
arge, he  says  it  has  given  off  one  atom  of  oxygen,  and  is 
now  a  molecule  of  litharge,  made  up  of  one  atom  of 
oxygen  and  one  atom  of  lead.  This  scandalises  his 
young  men,  who  have  been  brought  up  hi  the  belief 
that  size  (or  rather  lack  of  size)  is  of  the  essence  of  mole- 
cules, and  particularly  of  atoms.  My  colleague  defends 
himself  by  maintaining  that  his  meanings  are  not 
wrong,  but  merely  incomplete.  He  believes  that  the 
qualitative  approach  gives  the  students  a  much  better 
chance  of  getting  the  true  meaning  than  does  the  quanti- 
tative. In  the  ordinary  presentation  the  pupil  is  thrust 
into  the  middle  of  a  theory  before  he  realises  the  facts  of 
the  case.  In  very  many  instances  he  is  so  busy  whip- 
ping up  his  imagination  in  the  pursuit  of  the  incon- 
ceivably small  that  he  has  no  energy  or  interest  left  to 
attend  to  what,  after  all,  are  the  essentials  of  the  laws  of 
chemical  combination.  It  is  always  wise  to  begin  with 
the  proper  point  of  view  where  it  is  possible,  and  in 
this  case  it  is  not  only  possible  but  actually  easier  than 
what  may  not  unfairly  be  called  the  metaphysical 
approach. 

We  should  teach  by  good  example  rather  than  by  bad, 
by  showing  what  should  be  rather  than  by  showing  what 
should  not  be.  Positive  teaching  is  always  better  than 
negative.  The  "awful  example,"  as  it  is  called,  is  bad 
exposition  unless  under  conditions  in  which  there  is 
no  doubt  as  to  the  right  and  the  wrong.  To  write 
the  word  feild  on  the  blackboard  and  enlarge  on  the 
heinousness  of  spelling  it  in  that  way  only  strengthens 
the  chances  of  that  form  of  the  word  reappearing  in  the 
pupils'  exercise  books.  There  is  no  self-interpreting 
standard  compared  with  which  feild  will  stand  out  as 


ORDER  OF  PRESENTATION  221 

inherently  bad.  In  certain  forms  of  symmetrical  free- 
hand drawing,  on  the  other  hand,  common  errors  made 
by  the  pupils  may  be  with  safety  placed  upon  the  black- 
board, since  their  very  juxtaposition  to  the  model  will  at 
once  condemn  them.  There  is  here  an  objective  stand- 
ard to  which  appeal  may  be  made  with  no  fear  of 
misunderstanding.  So  with  the  objectionable  para- 
graph on  pages  205-207  of  this  chapter.  It  carries  its 
own  condemnation  with  it. 

In  dealing  with  grammatical  errors  the  type  should 
be:  "The  correct  form  is  'Charles  and  his  cavaliers 
were  defeated.' ':  The  emphasis  on  the  were  calls  atten- 
tion to  the  fact  that  this  is  correct,  without  recalling 
the  incorrect  was  of  the  exercise  book.  Even  in  a 
case  of  greater  difficulty,  where  there  might  be  room  for 
a  little  argument,  it  is  well  to  stick  to  the  positive  form. 
"  Charles  with  his  cavaliers  was  defeated . "  If  the  pupils 
themselves  raise  objections,  a  little  argument  may  be 
permitted,  but  even  then  the  repetition  should  always 
be  of  the  correct  form,  and  not  of  the  alternative 
were,  as  suggested  by  the  pupils.  Reiteration  of  the 
right  should  be  the  expositor's  principle  rather  than 
condemnation  of  the  wrong. 

Some  teachers  set  what  they  call  mistake-traps,  in 
order  to  illustrate  certain  forms  of  error.  The  condi- 
tions here  should  be  the  same  as  in  the  case  of  the  awful 
example.  Traps  should  never  be  set  unless  there  is  an 
objective  standard  to  which  the  wrong  answer  may 
be  referred.  These  traps  are  legitimate  only  in  those 
cases  in  which  matters  can  be  so  arranged  that  not  only 
shall  the  expected  mistake  occur,  but  it  shall  bring  its 
own  condemnation  with  it  by  confronting  itself  with 
some  irreconcilable  ideas  that  make  investigation  and 


222    EXPOSITION    AND  ILLUSTRATION  IN  TEACHING 

consequent  reconstruction  inevitable.  It  may  be  con- 
ceded that  so  long  as  a  mistake-trap  leads  the  mis- 
take maker  to  perceive  and  rectify  his  mistake,  no  harm 
is  done.  But  it  is  at  the  best  a  dangerous  form  of  exer- 
cise, and  when  used  should  always  be  followed  by  a  series 
of  exercises  leading  to  normal  results,  so  that  the  final 
impression  left  on  the  pupil's  mind  is  the  correct  one. 

It  is  a  favourite  charge  against  the  average  teacher 
that  he  is  too  fond  of  rules.  But,  after  all,  in  his  mind 
the  rule  occupies  only  the  second  place.  His  real  first 
love  is  the  exception.  All  his  professional  activities 
seem  to  centre  round  exceptions.  His  pupils,  indeed, 
acquire  from  the  teacher's  bias  a  distorted  view  of  the 
relative  values  of  rule  and  exception.  The  following 
dialogue  from  real  lif e  is  full  of  instruction :  — 

Teacher  (going  over  examination  paper  of  pupil  —  subject, 
French  Accidence).  I  see  you  have  given  generate  as  the  plural 
of  general.  Don't  you  know  that  nouns  in  -al  form  their  plural  in 
-auxl 

Pupil.  Yes,  sir,  but  I  thought  it  was  an  exception. 

Teacher.  But  what  made  you  think  it  was  an  exception  ? 

Pupil.  Because  it  was  set  in  the  examination,  sir. 

To  the  same  effect  is  the  advice  given  by  the  Scotch 
Dominie  to  the  promising  pupil  whom  he  is  sending 
up  to  the  Scholarship  Competition  at  Edinburgh  Uni- 
versity: — 

"When  in  doubt  mind  [remember]  that  practically 
everything  in  an  examination  governs  the  subjunc- 
tive." » 

No  doubt  the  demands  of  examinations  have  had  a 
great  deal  to  do  with  the  unhealthy  prominence  given 
to  exceptions.  Examiners  who  are  more  anxious  to 

1  Ian  Hay :  The  Right  Stuff,  p.  6. 


ORDER  OF  PRESENTATION  223 

show  what  a  candidate  does  not  know  than  to  find  out 
what  he  does,  have  naturally  a  warm  side  to  exceptions. 
But  the  teacher,  too,  is  not  without  guilt.  His  besetting 
virtue  is  accuracy,  and  he  cannot  bear  that  even  for  a 
time  his  pupil  should  be  told  something  that  will  not 
bear  the  fullest  investigation.  No  sooner  has  he  enun- 
ciated a  general  principle  than  some  wretched  excep- 
tion occurs  to  his  mind,  and  he  proceeds  with  indecent 
haste  to  modify  his  original  statement  by  indicating  in 
what  respect  it  comes  short  of  absolute  truth  as  known 
to  him.  Before  the  rule  has  time  to  be  established,  its 
authority  is  undermined.  The  old  Latin  grammars 
were  grossly  disloyal  to  their  rules.  In  a  couple  of  lines 
they  describe  the  behaviour  of  nine-tenths  of  the  words 
under  a  particular  category,  and  then  having  eased  their 
conscience  and  having  got  rid  of  the  herd  of  common- 
place words,  they  proceed  to  the  real  business  of  life  and 
wallow  in  exceptions.  The  exceptions  have,  of  course, 
a  place  in  teaching.  Fine  scholarship  is  determined, 
no  doubt,  just  by  the  accuracy  with  which  the  excep- 
tion is  treated.  But  in  a  procession,  mere  precedence 
does  not  determine  the  importance  of  the  people.  In 
some  processions  the  important  persons  come  first,  in 
others  last,  in  the  majority  the  important  place  is  some- 
where in  the  middle.  It  does  not,  therefore,  degrade  the 
exception  to  say  that  its  place  is  at  the  tail  of  the  pro- 
cession. The  rule  must  be  thoroughly  well  established 
before  the  exception  can  come  into  being.  We  may  in 
certain  forms  of  teaching  pass  from  the  example  to  the 
rule.  But  we  cannot  pass  from  the  exception  to  the 
rule.  For  if  we  try  to  do  so,  what  happens  is  that  we  for 
the  time  being  erect  the  exception  into  a  rule,  and  then 
bring  in  the  rule  as  an  exception. 


224    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

The  true  order  of  presentation  is  first  of  all  to  enun- 
ciate the  rule,  then  to  support  it.  The  rule  may  be 
either  given,  as  in  deductive  teaching,  or  worked  for, 
as  in  inductive.  In  either  case  it  must  be  buttressed 
up  with  many  examples,  and  not  weakened  by  any 
exceptions.  In  the  case  of  inductive  teaching  the  rule 
is  really  built  up  on  examples.  In  deductive  teaching 
it  is  justified  by  the  examples  adduced.  The  rule  should 
be  applied  in  many  ways,  all  involving  normal  examples 
of  its  working.  By  and  by  the  pupil  acquires  confi- 
dence in  his  rule,  and  treats  it  as  a  part  of  the  nature 
of  things.  Then  the  teacher  may  either  introduce  an 
exception,  or  merely  permit  his  vigilance  in  editing 
examples  to  relax,  and  allow  an  exception  to  occur  in 
the  ordinary  course  of  study.  Whether  the  exception 
occurs  by  accident  or  is  deliberately  introduced  by  the 
teacher,  the  detection  of  the  exception  should  be  left  to 
the  pupil.  Unless  the  pupil  is  struck  by  the  exception, 
as  an  exception,  the  rule  has  not  been  properly  assimi- 
lated. When  the  pupil  comes  to  complain  about  the 
rule  failing  hi  a  particular  case,  he  is  in  a  position  to  be 
told  of  the  nature  and  number  of  the  exceptions  for 
which  he  must  be  prepared.  It  will  be  noted  that  the 
pupil's  complaint  in  the  first  instance  will  not  be  against 
the  rule,  but  against  the  exception.  His  first  attitude  is 
and  ought  to  be  to  regard  the  exception  as  a  blunder  on 
the  part  of  some  one  or  other. 

Obviously  there  are  cases,  especially  in  dealing  with 
older  pupils,  when  it  may  be  permissible  to  introduce 
rule  and  exception  together.  This  is  especially  true 
when  the  rule  has  been  reached  by  an  examination  of  a 
great  series  of  examples,  and  when  the  number  of  excep- 
tions is  limited.  Suppose  the  pupil  has,  after  much 


ORDER  OF  PRESENTATION  225 

turning  up  of  the  dictionary,  come  to  the  conclusion 
that  most  German  substantives  that  are  dissyllabic 
and  that  end  in  e  are  feminine,  it  is  desirable  to  add 
on  the  spot  the  limitation  "not  denoting  members  of 
the  male  sex,"  and  to  give  the  exceptions  das  Auge, 
das  Ende,  and  das  Erbe.  On  the  other  hand,  the  ten 
German  substantives  now  ending  in  e  but  etymologi- 
cally  ending  in  n  should  be  left  to  be  discovered,  as 
exceptions  to  this  rule,  and  as  examples  of  a  rule  of 
their  own. 

So  far  we  have  been  dealing  with  Exposition  as  it 
affects  the  individual  mind.  The  problem  is  to  some 
extent  complicated  when  we  treat  of  exposition  to  a 
class.  The  same  principles  of  presentation  must,  of 
course,  hold  in  both  cases,  but  they  may  have  to  be 
differently  applied.  To  begin  with,  when  there  are 
from  twenty  to  sixty  minds  to  be  considered  (and  hi 
the  case  of  public  exposition  often  many  hundreds), 
it  is  clear  that  there  is  greater  difficulty  in  getting  at  the 
common  segment  of  mental  content.  In  the  case  of  a 
class  doing  ordinary  school  work  there  is  usually  much 
less  difficulty  on  this  score  than  one  might  expect. 
The  ground  has  already  been  prepared.  The  pupils 
are  of  approximately  the  same  age,  they  have  gone 
through  a  similar  course,  they  come  from  homes  that 
are  at  least  in  a  general  way  similar.  The  difficulty  in 
finding  common  ground  is  mainly  in  connection  with 
outside  matters,  and  is  felt  chiefly  in  introducing  more 
or  less  concrete  illustrations.  With  a  really  large  audi- 
ence the  expositor  must  adopt  the  purely  human  atti- 
tude. He  must  assume  in  his  hearers  only  the  most 
universal  qualities  of  human  nature,  and  whatever  de- 
gree of  knowledge  his  acquaintance  with  the  circum- 


226    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

stances  of  his  audience  may  warrant  him  in  assuming 
as  a  minimum. 

In  dealing  with  a  particular  mind,  we  may  approach 
it  on  one  particular  side  because  we  know  that  to  be  the 
most  accessible.  The  visual  and  the  audile,  for  example, 
would  be  approached  in  a  different  way;  but  with  a  class 
we  have  to  make  an  appeal  that  will  meet  all  needs. 
We  may  have  to  approach  a  subject  from  several  differ- 
ent points  in  turn,  hi  order  that  one  or  other  of  our 
approaches  may  appeal  to  the  different  members  of 
the  class.  We  may,  for  instance,  present  the  matter 
from  five  different  points  of  view.  It  is  probable  that 
some  of  the  really  capable  pupils  will  appreciate  all  the 
five  presentations.  Others  may  appreciate  only  four 
or  three  or  two  or  one.  It  may  chance  that  after  all 
there  may  be  one  or  two  hi  the  class  who  have  been  im- 
pervious to  all  five  modes  of  approach.  These  zeros 
may  be  safely  regarded  as  unfit  for  class  instruction, 
and  as  they  require  individual  treatment  maybe  neg- 
lected in  our  present  consideration. 

With  regard  to  the  others  there  is  the  serious  problem 
of  interest.  Especially  if  the  subject  is  not  in  itseli 
difficult,  it  becomes  very  tiresome  to  a  clever  boy  to 
have  it  explained  in  four  different  ways,  after  he  has 
mastered  it  at  the  first  exposition.  The  same  holds  oi 
the  other  pupils  for  all  the  explanations  given  aftei 
they  have  mastered  the  point  at  issue.  The  expositor  to 
a  class  must  therefore  lay  his  account  with  this  danger, 
and  do  what  he  can  to  introduce  a  second  line  of  inter- 
est that  may  compensate  the  quicker  pupils  for  theii 
enforced  retreading  of  the  old  ground.  It  has  to  be 
remembered  that  interest  does  not  arise  merely  in  the 
new  or  merely  in  the  old,  but  in  the  new  in  an  old  setting 


ORDER  OF  PRESENTATION  227 

or  the  old  in  a  new  setting.  By  the  conditions  of  the 
case  the  five  presentations  are  made  from  different 
points  of  view,  and  therefore  fulfil  to  some  extent  at 
least  the  conditions  on  which  interest  depends.  But  in 
the  actual  process  of  teaching  it  is  possible  to  introduce 
different  lines  of  interest.  The  quicker  pupils  may  be 
taken  into  the  teacher's  confidence  in  the  recapitula- 
tory presentations.  Questions  that  the  duller  pupils 
cannot  answer  because  they  have  not  yet  caught  the 
essential  point  may  be  answered  by  the  quicker  pupils 
to  their  own  satisfaction  and  to  the  edification  of  the 
duller  pupils.  What  is  a  line  of  investigation  and 
discovery  for  the  duller  pupils  may  well  be  a  course  of 
practical  applications  for  those  who  have  mastered  the 
principles  at  the  first  or  at  any  rate  at  one  of  the  earlier 
stages. 


CHAPTER  IX 
EXEMPLIFICATION  AND  ANALOGY 

NATURALLY  Illustration  must  observe  the  fundamen- 
tal principle  of  proceeding  from  the  known  to  the 
unknown.  We  must  approach  the  little  known  by 
means  of  the  better  known,  and  this  principle  must  over- 
ride all  others.  Probably  the  most  fundamental  mode 
of  Illustration  is  exemplification,  and  this  is  commonly 
understood  to  mean  the  illustration  of  the  rule  by  the 
presentation  of  examples.  It  would  seem  to  be  implied 
that  this  form  of  illustration  always  proceeds  deduc- 
tively. But  while  in  Exposition  we  may  be  said  to 
pass  from  the  rule  to  the  example,  in  Illustration  it 
would  seem  that  we  are  really  passing  from  the 
example  to  the  rule.  Of  the  two  the  example  is 
supposed  to  be  better  known  than  the  rule,  on  which 
as  a  matter  of  fact  it  casts  light.  When  we  say,  "  Will 
in  the  first  person  promises  or  threatens,  and  hi  the 
second  and  third  persons  simply  foretells:  as,  /  will  go 
in  spite  of  all  he  says.  He  mil  come  to  supper  to-night, " 
we  take  it  for  granted  that  the  person  we  are  speaking 
to  knows  the  shades  of  meaning  of  will  in  the  two  ex- 
amples as  a  mere  matter  of  experience  of  the  language, 
though  we  do  not  assume  that  he  knows  anything  about 
the  grammatical  statement  of  the  fact. 

But  in  practice  the  example  may  be  just  as  well  illus- 
trated by  the  rule  as  the  rule  by  the  example.  Every- 

228 


EXEMPLIFICATION  AND  ANALOGY  229 

thing  depends  upon  which  is  better  known  to  the  per- 
son we  are  dealing  with.  It  is  commoner,  no  doubt,  in 
ordinary  teaching  to  set  forth  a  general  rule  and  then 
follow  with  more  or  less  copious  examples.  But  it  is 
quite  as  useful  to  explain  a  puzzling  instance  by  refer- 
ring it  to  the  class  to  which  it  belongs,  in  other  words  by 
referring  it  to  the  rule  of  which  it  is  an  example.  When 
a  boy  on  the  classical  side  cannot  understand  the  mean- 
ing of  the  word  profaner  in  the  line, 

"Where  no  profaner  eye  may  look," 

the  master  may  make  matters  quite  clear  by  merely 
uttering  the  words  "Latin  comparative."  What  he 
has  done  is  to  refer  this  troublesome  example  to  a  rule 
that  he  knows  is  familiar  to  the  pupil.  When  a  less 
experienced  doctor  calls  in  a  more  experienced  one  to 
diagnose  a  difficult  case,  the  mere  mention  of  the  dis- 
ease by  the  older  practitioner  settles  the  matter  by 
referring  the  case  to  the  rule  of  which  it  is  an  example. 
Every  time  that  the  teacher  suggests  the  particular 
geometrical  proposition  that  will  solve  a  "rider,"  he  is 
really  illustrating  the  example  by  the  rule. 

When  we  are  told  in  the  dictionary  that  Illustration 
means  explaining  or  exemplifying  as  by  means  of  figures, 
comparisons,  and  examples,  it  would  seem  that  we  have 
a  twofold  classification  of  the  materials  of  Illustration. 
On  the  one  hand  there  are  comparisons  implying  like- 
ness and  unlikeness,  and  on  the  other  there  are  mere 
examples  that  owe  their  power  as  illustrations  to  the 
fact  that  they  show  some  rule  in  operation.  But 
after  all,  the  very  fact  that  the  different  examples  illus- 
trate the  same  rule  proves  that  they  have  something 
in  common,  and  that  therefore  the  idea  of  resemblance 


230    EXPOSITION   AND  ILLUSTRATION   IN  TEACHING 

is  present  in  them  also.  Aristotle  distinguishes  be- 
tween them,  calling  reasoning  by  example  paradigm 
and  reasoning  by  resemblance  analogy.  In  paradigm 
we  reason  from  one  example  to  another;  but  in  analogy 
we  reason  from  a  more  clearly  stated  resemblance. 
With  Aristotle  analogy  is  treated  as  equivalent  to 
mathematical  proportion,  which  involves  the  equality 
of  ratios. 

Our  whole  experience  is  intelligible  only  on  the  as- 
sumption that  the  operations  of  mind  and  matter  are 
regulated  according  to  certain  laws  that  act  uniformly. 
The  law  remains  the  same  though  the  cases  of  its  appli- 
cation vary  as  to  what  may  be  called  content.  When 
therefore  we  find  a  particular  law  acting  in  connection 
with  one  content  we  assume  that  the  same  law  will 
hold  under  similar  conditions  in  connection  with  another 
content.  The  selection  of  the  common  element  from 
two  disparate  cases  is l  naturally  very  difficult.  For  pur- 
poses of  illustration,  therefore,  it  is  well  to  adopt  the 
Aristotelian  view  of  analogy  as  limited  to  the  equality 
of  ratios.  This  enables  us  to  express  all  illustrative 
analogies  in  mathematical  terms,  as  thus,  a  :  b  : :  c  :  d. 
Now  if  a  has  the  same  relation  to  6  that  c  has  to  d,  and 
the  pupil  knows  either  the  relation  that  a  has  to  6  or  the 
relation  that  c  has  to  d,  the  teacher  is  in  a  position  to 
illustrate  the  unknown  relation  by  a  reference  to  the 
known.  In  the  case  in  which  the  pupil  knows  both  of 
the  relations,  the  teacher  is  still  able  to  use  the  analogy 
as  an  illustration,  but  in  this  case  the  purpose  will  be 

1  Cf .  F.  H.  Bradley :  "  The  real  axiom  of  identity  is  this :  What  is 
true  in  one  context  is  true  in  another;  or,  If  any  truth  is  stated  so  that  a 
change  in  events  will  make  it  false,  then  it  is  not  a  genuine  truth  at 
all."  —  The  Principks  of  Logic,  p.  133. 


EXEMPLIFICATION  AND  ANALOGY  231 

rather  the  aesthetic  satisfaction  of  the  pupil  than  the 
clarifying  of  his  ideas. 

In  ordinary  life  all  that  great  series  of  shorthand 
thinking  that  is  represented  by  proverbial  philosophy 
is  based  upon  the  assumption  that  metaphor  does 
carry  a  certain  amount  of  weight  as  argument.  "You 
cannot  make  a  silk  purse  out  of  a  sow's  ear"  may  have 
no  direct  connection  with  the  case  of  the  nobleman 
who  marries  his  kitchenmaid;  but  the  plain  man  is 
satisfied  that  when  he  has  quoted  the  proverb  he  has 
said  something  to  the  point  in  this  connection.  He 
feels  that  he  has  at  least  made  matters  clearer,  has 
thrown  light  upon  the  subject,  has  illustrated  it. 

As  metaphor  by  its  very  nature  deals  entirely  with 
relations,  it  is  obviously  of  the  first  importance  in 
Illustration.  It  is,  in  fact,  in  all  cases  an  instance  of 
Aristotelian  analogy.  The  proverb  may  be  represented 
in  purely  mathematical  form :  — 

sow's  ear  :  silk  purse  : :  kitchenmaid  :  noblewoman. 

The  implication  is  that  the  relation  between  the  sow's 
ear  and  the  silk  purse  is  the  same  as  that  between  the 
kitchenmaid  and  the  noblewoman  ;  that  is,  that  the 
one  cannot  be  turned  into  the  other.  As  an  argument, 
this  metaphor  is  unsatisfactory,  and  as  an  illustration 
its  value  is  mainly  aesthetic.  It  gives  satisfaction  by 
stating  in  a  very  effective  way  what  a  great  many  peo- 
ple believe  to  be  true.  In  this  case  it  is  assumed  that 
we  know  both  terms  of  the  analogy,  but  in  most  cases 
of  what  may  be  called  illustrative  metaphors  in  teach- 
ing, one  pair  of  terms  is  assumed  to  be  better  known 
than  the  other.  We  have  seen  that  it  does  not  matter 
which  pair  is  known,  the  only  important  point  being 


232    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

that  one  pair  must  be  better  known  than  the  other. 
When  we  speak  of  being  better  known,  it  should  be  un- 
derstood that  we  are  referring  to  knowledge  of  the  rela- 
tion. For  a  metaphor  to  have  any  illustrative  value  at 
all,  the  pupil  must  know  all  four  terms  as  terms,  though 
the  true  relation  between  one  of  the  pairs  may  not 
be  known  by  him.  Naturally  the  less  known  relation 
must  take  its  place  as  the  illustrandum.  There  is  this 
further  point,  that  the  person  using  the  illustration  is 
supposed  to  know  the  relationship  between  the  terms 
in  both  parts  of  the  metaphor,  and  to  vouch  for  the 
resemblance  of  those  ratios.  As  a  method  of  discovery, 
analogy  may  not  always  be  quite  reliable,  but  as  a 
means  of  illustration  there  is  no  justification  for  its 
ever  misleading,  so  long  as  it  is  skilfully  used.  The 
source  of  error  in  teaching  is  quite  different  from  that 
in  discovery. 

An  illustrative  analogy  that  misleads  usually  does  so 
through  a  process  of  spreading  that  is  characteristic  of 
all  untrained  minds.  It  is  not  enough  that  the  relation 
between  the  two  terms  in  the  first  branch  of  the  anal- 
ogy is  identical  with  that  between  the  two  terms  in  the 
second:  this  relation  must  be  kept  within  the  bounds 
of  the  particular  analogy.  The  tendency  of  the  mind 
is  to  supply  a  great  many  subordinate  analogies,  and 
to  hold  them  as  of  equal  importance  with  the  original. 
In  other  words,  the  illustrative  analogy  is  really  an 
abstraction  which  the  ordinary  mind  tends  to  make 
concrete  by  adding  on  a  great  number  of  qualities  to 
each  pan*  of  terms,  and  insisting  that  a  series  of  parallel 
analogies  shall  hold  between  the  different  pairs.  Thus 
Professor  James's  figure  of  the  stream  of  consciousness 
has  been  condemned  because  our  thoughts  do  not  pass 


EXEMPLIFICATION  AND  ANALOGY  233 

once  for  all  through  the  mind,  and  never  come  back. 
The  critic  would  substitute  the  figure  of  a  cistern,  be- 
cause the  mind  is  rather  a  reservoir  from  which  old 
thoughts  can  be  drawn  at  will.  Obviously  the  cistern- 
figure  may  be  condemned  in  its  turn,  on  the  ground  that 
our  thoughts  do  not  stagnate  like  the  water  in  a  cistern : 
while  the  ideas  that  we  draw  from  the  mind  we  do  not 
throw  away  forever  after  using  as  we  do  with  the  water 
we  have  drawn  from  a  cistern.  An  illustration  should 
be  a  perfect  analogy  as  far  as  it  goes,  but  it  must  be 
limited  to  the  relations  that  give  it  meaning.  James's 
figure  was  introduced  to  illustrate  the  fact  that  the 
contents  of  consciousness  have  bulk:  our  ideas  do 
not  form  mere  series,  but  rather  masses.  This  is  well 
brought  out  by  the  figure  of  the  river  (James,  in  fact, 
goes  the  length  of  giving  an  illustrative  section1  of  the 
stream),  but  to  carry  over  the  details  is  to  court  error. 
One  might  as  well  object  that  our  ideas  are  not  wet,  as 
they  would  necessarily  be  if  they  formed  part  of  a  river. 

The  case  has  been  epigrammatically  put :  "  If  a  meta- 
phor will  go  with  you  a  mile,  do  not  compel  it  to  go  with 
you  twain." 

No  doubt  very  elaborate  analogies  are  sometimes 
used,  and  worked  out  in  much  detail.  Our  great  alle- 
gories, for  instance,  give  many  excellent  examples  of 
analogy  skilfully  maintained  for  long  stretches  at  a 
time.  But  in  all  such  cases  sooner  or  later  the  analogy 
breaks  down,  and  gives  an  opportunity  for  the  critic 
to  find  serious  fault.  It  is  here  that  the  deliberately 
constructed  illustrative  story  or  parable  calls  for  criti- 
cism. Such  stories  as  Professor  Drummond's  Baxter's 
Second  Innings  have  to  be  judged  from  two  different 

1  Principles  of  Psychology,  Vol.  I,  p.  279. 


234    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

standpoints:  first  as  works  of  art,  secondly  as  more  or 
less  consistent  analogies,  with  a  moral  purpose.1 

Teaching  by  metaphor,  in  spite  of  Aristotle's  praise  of 
that  figure,2  has  its  dangers  and  must  be  confined  to  the 
essentials  of  the  relationship  to  be  illustrated;  and  in 
order  to  keep  one  metaphor  within  its  proper  bounds, 
it  is  desk-able  that  it  should  be  balanced  by  other  meta- 
phors. The  relation  between  mind  and  mental  content 
may  be  illustrated  by  reference  to  a  river,  a  well,  a 
reservoir,  a  kaleidoscope,  a  blank  sheet  of  note-paper,  a 
stage,  a  dome,  a  photographer's  plate.  Each  figure  as 
it  is  used  is  corrected  by  the  others,  and  only  the  really 
essential  relationship  is  left  in  the  reader's  mind.  Each 
of  the  figures  marks  a  certain  aspect  of  the  truth,  but 
while  each  emphasises  its  own  aspect  it  tends  to  restrict 
the  application  of  all  the  others  to  their  own  proper 
place.  The  common  elements  in  all  the  figures  fuse, 
while  the  peculiarities  of  each  are  arrested  by  the 
peculiarities  of  the  others. 

This  advance  by  means  of  fusion  and  arrest  is  often 
applied  in  dealing  with  ordinary  school  subjects.  The 
symmetry  of  many  algebraic  results  is  thus  made  pat- 
ent to  the  pupil  without  the  direct  intervention  of  the 
teacher.  The  familiar  formula  (a+6)2  =  a2  +  2  ab  +  b2 
may  be  insinuated  into  the  pupil's  mind  by  a  series 
of  actual  multiplications,  the  letters  being  changed 
in  each  case.  The  purely  general  character  of  the  re- 
sult soon  becomes  clear,  and  the  pupil  sees  that  it  is 

1  This  subject  receives  fuller  treatment  in  Chapter  X. 

2  "  But  the  greatest  thing  by  far  is  to  have  a  command  of  meta- 
phor.    This  alone  cannot  be  imparted  by  another;   it  is  the  mark  of 
genius,  —  for  to  make  good  metaphors  implies  an  eye  for  resem- 
blances."— Poetics,  Vol.  XXII,  p.  9;  S.  H.  Butcher's  translation. 


EXEMPLIFICATION   AND  ANALOGY  235 

unnecessary  to  do  the  actual  multiplication  in  order 
to  reach  the  desired  result.  The  analogy  forces  itself 
upon  his  notice. 

In  order  that  a  metaphor  may  have  its  full  value  as  an 
illustration,  the  analogy  must  be  completely  presented 
to  the  mind;  i.e.  both  pah's  of  terms  must  be  given  at 
the  same  time.  Even  if  each  pair  is  familiar  to  the 
mind  dealt  with,  they  must  be  presented  together  in 
order  that  they  may  produce  their  proper  effect. 
Unless  this  is  done,  the  metaphor  presents  itself  not  as 
an  illustration  but  as  a  problem.  This  becomes  clear 
if  we  take  one  or  two  examples  of  the  illustration  with- 
out indicating  the  illustrandum :  — 

"He  clasps  the  crag  with  crooked  hands; 
Close  to  the  sun  in  lonely  lands, 
Ring'd  with  the  azure  world  he  stands. 
The  wrinkled  sea  beneath  him  crawls ; 
He  watches  from  his  mountain  walls, 
And  like  a  thunderbolt  he  falls.1 " 

Till  we  are  told  that  Tennyson  is  here  dealing  with  the 
eagle,  we  experience  a  sense  of  discomfort.  The  natural 
effect  of  the  personal  pronoun  is  to  suggest  a  human 
background  for  the  presented  ideas,  and  we  find  it  diffi- 
cult to  make  a  picture  that  will  satisfy  us  by  combining 
in  a  reasonable  way  all  the  materials  supplied.  So  soon, 
however,  as  we  get  the  key  to  the  problem,  we  find  a 
great  deal  of  pleasure  in  tracing  out  the  parallelism. 
Given  a  relation,  it  is  not  very  difficult  to  find  a  parallel 
that  will  illustrate  this  relation.2  But  given  an  illustra- 

1  A  Fragment,  Tennyson's  Works,  1883,  p.  134. 

2  Jean  Paul  Richter  appears  to  take  a  different  view  in  the  following 
passage  from  the  Vorschule  der  dZsthetik,  Programm  IX,  Section  50 :  — 
"Geht  ein  Dichter  durch  ein  reifes   Kornfeld  spazieren:   so  werden 


236    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

tion,  it  may  be  almost  impossible  to  find  the  original 
relation  which  is  to  be  illustrated,  though  when  the 
relation  is  discovered,  the  beauty  of  the  comparison 
may  be  easily  appreciated.  The  mental  process  is  dif- 
ferent in  the  two  cases.  In  appreciating  the  compari- 
son we  are  dealing  with  perception  and  apperception: 
in  seeking  for  the  relation  that  is  illustrated,  we  are 
dealing  with  discovery.  In  the  first  case  we  have  to  fol- 
low a  lead  that  is  given :  in  the  second  we  have  to  pass 
from  an  effect  to  a  cause,  where  many  causes  may  lead 
to  the  same  effect,  and  yet  only  one  cause  will  meet  the 
case  in  point.  Take  the  following  example  of  a  series 
of  metaphors  referring  to  an  historical  character:  — 

"That  grand  impostor,  that  loathsome  hypocrite,  that  detest- 
able monster,  that  prodigy  of  the  universe,  that  disgrace  of  man- 
kind, that  landscape  of  iniquity,  that  sink  of  sin,  and  that  com- 
pendium of  baseness  —  " 

This  has  the  air  of  being  a  comparatively  easy  case. 
It  would  appear  that  from  the  superlative  nature  of 
the  figures  used  there  could  hardly  be  two  men  in  the 

ihn  die  aufrechten  und  korner-armen  JEhren  leicht  zu  dem  Gleichniss 
heben,  dass  sich  der  leere  Kopf  eben  so  aufrichte  .  .  .  aber  er  wird 
einige  Muhe  haben,  fur  denselben  Gedanken  eines  zugleich  unbedeu- 
tenden  und  doch  stolzen  Menschen  in  den  unabsehlichen  Korper- 
Reihen  auf  den  Schieferabdruck  jener  Blume  zu  treffen."  But  every- 
thing depends  upon  the  state  of  the  mental  content  of  the  person 
concerned.  If  the  teacher  asks  a  class  what  the  haughtily  upright 
but  poorly  filled  ears  of  corn  make  one  think  of,  it  is  quite  likely  that 
he  will  get  several  pupils  to  suggest  empty-headed,  pompous  people, 
but  by  emphasising  the  two  qualities  of  emptiness  and  stiffness  he 
has  really  suggested  the  comparison.  On  the  other  hand,  if  he  asks 
a  class  to  find  an  illustration  among  plants  of  an  insignificant  but  pom- 
pous person,  not  many  of  his  pupils  would  suggest  corn  at  all,  but 
there  would  be  little  lack  of  quite  suitable  comparisons  with  other 
plants,  mainly  flowers. 


EXEMPLIFICATION  AND  ANALOGY  237 

world  who  could  fill  the  part.  Yet  if  this  description  is 
proposed  to  a  class  of  senior  pupils  as  a  problem,  it  is 
astonishing  how  many  fairly  intelligent  attempts  may 
be  made  without  any  pupil  hitting  upon  the  truth. 
King  John  is  often  selected;  Nero  is  a  favourite  sugges- 
tion; and  Judas  Iscariot  may  by  many  be  regarded  as 
a  better  answer  than  the  real  one.  We  require  the 
further  hint  that  the  words  are  those  of  the  stout  old 
cavalier,  Sir  Henry  Lee,1  before  we  can  apply  them  to 
Oliver  Cromwell. 

As  soon  as  we  have  found  the  key,  we  see  how  true  the 
comparison  is  —  from  Sir  Henry's  point  of  view.  But 
in  the  following  example,  from  one  of  Charles  Lamb's 
essays,  we  have  a  series  of  epithets  that  are  in  most  cases 
wonderfully  apposite.  When  we  know  the  subject  re- 
ferred to,  we  admit  that  at  least  twenty  of  the  twenty- 
seven  metaphors  are  admirably  suited  to  illustrate  that 
subject.  Yet  after  reading  these  twenty-seven  illumi- 
nating metaphors  without  being  told  the  subject,  most 
readers  find  it  impossible  to  discover  what  they  all  refer 
to.  That  is  to  say  that  a  given  relation  is  illustrated 
by  twenty-seven  parallels  —  of  which  at  least  twenty 
are  excellent  —  without  making  it  possible  for  the 
average  man  to  find  out  what  that  relation  is.  The 
reader  probably  remembers  the  essay  in  question,  but 
he  cannot  do  better  than  try  the  experiment  of  reading 
to  his  most  intelligent  friends  (or  to  a  class,  if  one  is 
available)  the  following  description,  and  asking  them  to 
say  what  is  the  subject  of  the  first  is:  — 

" is  the  most  irrelevant  thing  in  nature  —  a  piece  of  im- 
pertinent correspondency  —  an  odious  approximation  —  a  haunting 
conscience  —  a  preposterous  shadow,  lengthening  in  the  noontide  of 

1  Scott :  Woodstock,  Chap.  XXV. 


238    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

our  prosperity  —  an  unwelcome  remembrancer  —  a  perpetually 
recurring  mortification  —  a  drain  on  your  purse,  a  more  intolerable 
dun  upon  your  pride  —  a  drawback  upon  success  —  a  rebuke  to  your 
rising  —  a  stain  in  your  blood  —  a  blot  on  your  'scutcheon  — a  rent 
in  your  garment  —  a  death's  head  at  your  banquet  —  Agathocles' 
pot  —  a  Mordecai  in  your  gate,  a  Lazarus  at  your  door  —  a  lion  in 
your  path  —  a  frog  in  your  chamber  —  a  fly  in  your  ointment  —  a 
mote  in  your  eye  —  a  triumph  to  your  enemy,  an  apology  to  your 
friends  —  the  one  thing  not  needful  —  the  hail  in  harvest  —  the 
ounce  of  sour  in  a  pound  of  sweet." 

In  spite  of  the  cumulative  effect  of  twenty-seven 
broad  hints,  you  will  almost  certainly  find  that  your 
friends  or  pupils  fail  to  arrive  at  the  true  subject. 
This  looks  as  if  Lamb's  ingenious  series  of  metaphors 
was  of  little  value  in  illustrating  his  subject.  Yet  the 
moment  the  reader  or  hearer  knows  that  this  subject  is 
A  Poor  Relation,  he  finds  that  every  one  of  the  epithets 
does  something  towards  clearing  up  his  ideas  on  the 
subject.  The  process  of  selecting  from  each  of  these 
figures  the  element  that  is  common  to  all  —  the  fun- 
damental relationship  —  is  of  the  utmost  service  in 
throwing  light  upon  the  relationship. 

In  his  essay,  Lamb  mercifully  begins  with  the  subject, 
so  that  his  epithets  are  read  with  pleasurable  interest. 
Sometimes,  however,  a  writer,  but  more  frequently  a 
speaker,  deliberately  uses  a  suppressed  subject  in  order 
to  enhance  the  interest  of  his  words.  This  is  obviously 
a  special  application  of  the  principle  of  the  vacuum,  and 
if  skilfully  applied,  the  method  is  quite  justifiable.  It 
is  a  challenge  from  the  speaker  to  his  hearers,  and  a 
great  part  of  the  charm  of  the  problem  is  the  activity 
it  encourages  within  narrow  limits.  As  a  problem  it 
should  be  presented  in  such  a  way  as  not  to  be  so  diffi- 
cult as  the  passage  from  Lamb  would  be,  if  uttered  in 


EXEMPLIFICATION   AND  ANALOGY  239 

its  present  form  before  an  audience.  It  must  be  possible 
for  the  abler  among  the  audience  to  solve  the  problem 
before  the  passage  is  completed.  More  or  less  broad 
hints  should  be  given  throughout,  and  the  circum- 
stances of  the  case  should  also  supply  a  certain  guidance. 
It  will  be  readily  admitted  that  these  hints  have  a  ten- 
dency to  help  each  other,  so  that  their  influence  is 
cumulative,  as  in  the  parlor  game  of  "Lights"  in  which 
two  persons  begin  talking  round  some  subject  that  is 
not  revealed  to  the  rest  of  the  company.  The  subject 
is  never  mentioned  by  name,  but  each  person  who  thinks 
he  has  guessed  it,  from  what  he  has  heard  of  the  con- 
versation, joins  in  and  tests  by  the  relevancy  of  his 
remarks  whether  his  guess  is  right  or  wrong.  Obviously 
the  longer  the  conversation  lasts  the  greater  the  chance 
of  the  auditors  to  discover  the  subject,  but  all  the  time 
their  wits  must  be  actively  employed  if  they  hope  for 
success. 

An  excellent  example  of  this  form  of  illustrative 
teaching  is  supplied  by  an  address  given  by  Dr.  William 
Osier  to  medical  students.  The  reader  should  experi- 
ment with  himself,  and  note  the  exact  point  at  which  he 
guesses  the  word,  and  the  point  at  which  he  is  sure  that 
his  guess  is  right.  In  order  to  prevent  the  possibility 
of  the  reader's  eye  catching  the  actual  word,  it  is  repre- 
sented by  a  dash  in  the  text,  but  is  given  in  a  footnote 
that  will  be  found  when  the  page  is  turned : 


THE  MASTER-WORD 

"  It  seems  a  bounden  duty  on  such  an  occasion  to  be  honest  and 
frank,  so  I  propose  to  tell  you  the  secret  of  life  as  I  have  seen  the 
game  played,  and  as  I  have  tried  to  play  it  myself.  You  remember 


240    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

in  one  of  the  Jungle  Stories  that  when  Mowgli  wished  to  be  avenged 
on  the  villagers,  he  could  only  get  the  help  of  Hathi  and  his  sons  by 
sending  them  the  master-word.    This  I  propose  to  give  you  in  the 
hope,  yes,  in  the  full  assurance,  that  some  of  you  at  least  will  lay 
hold  upon  it  to  your  profit.    Though  a  little  one,  the  master-word 
looms  large  in  meaning.     It  is  the  open-sesame  to  every  portal,  the 
great  equaliser  in  the  world,  the  true  philosopher's  stone,  which 
transmutes  all  the  base  metal  of  humanity  into  gold.     The  stupid 
man  among  you  it  will  make  bright,  the  bright  man  brilliant,  and 
the  brilliant  student  steady.     With  the  magic  word  in  your  heart 
all  things  are  possible,  and  without  it  all  study  is  vanity  and  vexa- 
tion.   The  miracles  of  life  are  with  it ;  the  blind  see  by  touch,  the 
deaf  hear  with  eyes,  and  the  dumb  speak  with  fingers.    To  the  youth 
it  brings  hope,  to  the  middle-aged,  confidence,  to  the  aged,  repose. 
True  balm  of  hurt  minds,  in  its  presence  the  heart  of  the  sorrowful 
is  lightened  and  consoled.     It  is  directly  responsible  for  all  advances 
in  medicine  during  the  past  twenty-five  centuries.     Laying  hold 
upon  it,  Hippocrates  made  observation  and  science  the  warp  and 
woof  of  our  art.    Galen  so  read  its  meaning  that  fifteen  centuries 
stopped  thinking  and  slept,  till  awakened  by  the  'De  Fabrica' 
of  Vesalius,  which  is  the  very  incarnation  of  the  master-word. 
With  its  inspiration  Harvey  gave  an  impulse  to  a  larger  circulation 
than  he  wot  of,  an  impulse  which  we  feel  to-day.    Hunter  sounded 
all  its  heights  and  depths,  and  stands  out  in  our  history  as  one  of 
the  great  exemplars  of  its  virtue.  .  .  .    Not  only  has  it  been  the 
touchstone  of  progress,  but  it  is  the  measure  of  success  in  everyday 
life.     Not  a  man  before  you  but  is  beholden  to  it  for  his  position  here, 
while  he  who  addresses  you  has  that  honour  directly  in  consequence  of 
having  had  it  graven  on  his  heart  when  he  was  as  you  are  to-day. 
And  the  master-word  is  — ,  a  little  one,  as  I  have  said,  but  fraught 
with  momentous  sequences,  if  you  can  but  write  it  on  the  tablets  of 
your  hearts,  and  bind  it  upon  your  foreheads."  * 

These  one-sided  metaphors  illustrate  clearly  what 
Aristotle  means  when,  after  praising  the  use  of  meta- 
phors as  indicating  high  intelligence,  he  goes  on  to  say 
that  as  a  style  made  up  entirely  of  strange  or  rare  words 

1  jEquanimitas  and  Other  Addresses,  p.  373. 


EXEMPLIFICATION   AND   ANALOGY  241 

is  a  jargon,  so  a  style  made  up  entirely  of  metaphors 
becomes  a  riddle. 

"  For  the  essence  of  a  riddle  is  to  express  true  facts  under  impos- 
sible combinations.  Now  this  cannot  be  done  by  any  arrangement 
of  ordinary  words,  but  by  the  use  of  metaphor  it  can."  l 

There  arises  here  an  interesting  application  of  the 
principles  of  the  order  of  presentation.  It  is  clearly 
important  for  the  illustrator  to  determine  whether  he 
ought  to  begin  with  the  illustration  or  the  illustrandum. 
Logically,  the  main  idea  should  come  first  and  the  illus- 
trative matter  should  follow.  But  it  is  interesting  to 
observe  that  in  actual  practice  the  poets  are  rather 
fond  of  inverting  this  order.  "  As  "  is  the  natural  begin- 
ning of  a  poetical  comparison,  and  the  illustrandum  is 
generally  held  back  till  the  correlative  "so"  introduces 
it.  We  are  sometimes  told  that  in  the  poet's  own  think- 
ing the  process  is  reversed,  but  it  is  very  probable  that 
in  the  case  of  our  finer  poets  the  figure  frequently 
precedes  in  thought  as  it  precedes  in  expression.2  In 
any  case  it  suits  the  poet's  purpose  to  put  the  figure  in 
the  foreground,  when  he  is  making  his  presentation :  — 

"Thus  presented,  it  gives  more  cohesion  to  the  poetic  period, 
rouses  curiosity,  holds  it  in  suspense  to  the  end ;  one  must  get  to 

1  Poetics,  XXII,  2. 

2  The  account  of  the  manufacture  of  The  Raven  in  E.  A.  Poe's 
fascinating  essay  on  The  Philosophy  of  Composition  must  be  taken 
with  some  caution.     No  doubt  some  poems  have  been  built  up  in  this 
way.     But  they  are  not  of  very  high  rank.     The  essay  is  full  of  value 
for  the  didactic  illustrator,  but  is  of  little  use  to  the  poet.     Poe  has 
the  didactic  instinct  very  strongly  developed.     Probably  he  was  not 
thinking  of  himself  when  he  wrote:  "It  is  the  curse  of  a  certain  order 
of  mind  that  it  can  never  rest  satisfied  with  the  consciousness  of  its 
ability  to  do  a  thing.     Not  even  is  it  content  with  doing  it.     It  must 
both  know  and  show  how  it  was  done."     Marginalia,  XLVII. 

R 


242    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

the  second  part  of  the  period  in  order  to  understand  its  meaning; 
in  place  of  which,  if  one  presents  the  principal  idea  at  first,  the 
figure  coming  afterwards,  not  being  expected,  will  have  the  effect  of 
a  mere  after-thought  [hors-d'oeuvre]."  1 

It  is  clear  that  we  are  here  dealing  with  the  aesthetic 
use  of  illustration.  But  when  we  come  to  the  didactic 
use,  we  must  bring  the  illustrandum  into  the  first  rank. 
Here  the  purpose  is  not  mere  enjoyment,  but  clear 
thinking  ;  not  a  conundrum,  but  an  exposition.  Till 
he  knows  what  is  being  illustrated,  the  pupil  cannot 
understand  the  illustration  as  illustration.  Accordingly, 
he  is  exposed  to  all  the  temptations  to  set  up  premature 
conceptions,  and  will  thus  have  to  do  over  again  all  his 
thinking,  as  soon  as  he  finds  the  real  point  at  issue.  This 
is  precisely  what  we  have  seen  in  the  previous  chapter 
is  to  be  specially  avoided.  No  doubt  in  the  process 
of  discovery  and  invention  we  are  frequently  thrown 
out  of  our  reckoning,  and  have  to  rethink  our  thoughts. 
But  when  we  are  being  taught  in  the  sense  of  having 
something  expounded  to  us,  we  have  a  right  to  expect 
that  we  shall  not  be  misled  by  the  person  who  professes 
to  be  our  guide. 

In  teaching,  it  may  be  desirable  as  a  general  rule  to 
pass  from  particular  cases  to  general  conclusions  or  prin- 
ciples. But  there  are  cases  in  which  it  is  better  to  start 
with  a  clear  statement  of  the  principle  and  then  proceed 
to  illustrate  it.  An  excellent  example  of  the  clear  state- 
ment of  a  principle  followed  by  a  very  ingenious  illus- 
tration is  to  be  found  in  Part  III  of  De  Quincey's 
Essay  on  Style.  Starting  from  the  principle  which 
he  finds  in  Paterculus  that  there  is  a  tendency  of  intel- 
lectual power  to  gather  in  clusters,  he  illustrates  this 

1  Paul  Souriau :  La  Suggestion  dans  V  Art,  p.  227. 


EXEMPLIFICATION   AND  ANALOGY  243 

summarily  by  referring  to  the  three  great  periods  in  Eng- 
lish literature:  the  Elizabethan,  the  Queen  Anne,  and 
the  period  beginning  with  Cowper  ;  and  then  proceeds 
to  give  one  of  the  most  ingeniously  manipulated  illus- 
trations to  be  found  anywhere.  The  two  great  clusters 
of  Greek  intellect  centre  each  round  one  man  ;  the  first 
round  Pericles,  the  second  round  Alexander  of  Macedon. 
"On  good  reasons,  not  called  for  in  this  place,"  he  tells 
us  that  the  year  444  B.C.  is  the  most  suitable  locus 
for  Pericles,  while  the  annus  mirabilis  of  Alexander's 
life  was  the  year  333  B.C.  The  Pericles  cluster  is  thus 
described :  — 

"First  come  the  three  men,  divini  spiritus,  under  a  heavenly 
afflatus,  ^Eschylus,  Sophocles,  Euripides,  the  creators  of  Tragedy 
out  of  a  village  mummery ;  next  comes  Aristophanes,  who  breathed 
the  breath  of  life  into  Comedy ;  then  comes  the  great  philosopher, 
Anaxagoras,  who  first  theorised  successfully  upon  man  and  the 
world.  Next  come,  whether  great  or  not,  the  still  more  famous 
philosophers,  Socrates,  Plato,  Xenophon ;  then  comes,  leaning  upon 
Pericles  as  sometimes  Pericles  leaned  upon  him,  the  divine  artist 
Phidias ;  and  behind  this  immortal  man  walk  Herodotus  and  Thu- 
cydides." 

The  Alexandrine  cluster  is  not  quite  so  brilliant,  but 
De  Quincey  makes  capital  play  with  the  two  central 
figures,  Aristotle  and  Demosthenes.  Next  comes  Lysip- 
pus,  the  sculptor,  and  Apelles,  the  painter.  No  other 
names  are  mentioned  :  a  testimonial  to  De  Quincey's 
honesty.  Names  could  be  easily  given,  but  as  they  do 
not  stand  for  men  of  quite  the  same  rank  as  the  men  of 
the  Periclean  cluster,  we  are  merely  told  that  "there  are 
now  exquisite  masters  of  the  more  refined  comedy," 
and  "historians  there  are  now  as  in  that  former  age." 
Pericles  is  well  balanced  by  "Alexander  himself,  with  a 


244    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

glittering  cortege  of  general  officers  well  qualified  to 
wear  the  crowns  which  they  will  win." 

Having  now  got  his  two  clusters,  De  Quincey  pro- 
ceeds to  unite  them  under  the  figure  of  the  two  balls  of 
a  dumb-bell,  the  cylindrical  bar  joining  them  being 
represented  by  the  orator  Isocrates,  pater  eloquentice 
and  communis  magister  oratorum,  Milton's  "that  old 
man  eloquent"  who,  thanks  to  weak  lungs  and  con- 
stitutional cowardice,  contrived  to  keep  out  of  trouble 
long  enough  to  have  a  personal  acquaintance  with  the 
great  men  of  both  clusters.  The  aged  orator  had  seen 
twenty-four  Olympiads,  and  therefore  quite  satisfac- 
torily bridged  the  111  years  that  separated  444  B.C. 
from  333  B.C.  It  would  be  difficult  to  find  a  more  in- 
genious and  —  perhaps  with  the  exception  of  that  sup- 
pressed reason  for  the  choice  of  the  date  444  B.C.  — 
a  fairer  illustration  of  Paterculus's  thesis.  Every  ex- 
perienced teacher  will  appreciate  its  practical  value. 

While  a  material  illustration  like  that  of  the  dumb- 
bell is  frequently  very  effective  in  such  a  connection  as 
that  in  which  De  Quincey  uses  it,  we  get  greater  help 
from  it  when  we  keep  to  the  region  of  the  material. 
There  it  has  a  compelling  power  that  it  lacks  in  more 
abstract  connections.  It  would  require  a  very  great 
deal  of  writing  to  convey  the  same  accurate  effect  as 
is  produced  by  the  following  illustration :  — 

"The  battle  was  fought  as  though  the  British  troops  were  travel- 
ling along  the  radii  of  a  fan,  of  which  the  French  constituted  the 
outer  circumference.  As  the  fight  progressed,  the  fan  commenced 
to  contract." 

There  is,  unfortunately,  an  ambiguity  involved  in  the 
one  word  contract.  As  a  matter  of  experiment  with  an 
intelligent  class  of  students  (age  21-24)  I  found  that 


EXEMPLIFICATION  AND  ANALOGY  245 

about  a  third  regarded  the  figure  as  implying  that  the 
fan  began  to  get  smaller  from  tip  to  circumference,  or, 
in  other  words,  by  the  diminution  in  the  length  of  the 
radii.  The  substitution  of  the  word  close  for  con- 
tract removes  all  possibility  of  misunderstanding  the 
expositor's  meaning.  A  figure  like  this  is  a  sort  of  un- 
drawn diagram.  A  few  lines  on  a  blackboard  would 
make  the  matter  equally  clear,  but  in  cases  where  a 
certain  shape  (in  this  case,  the  fan)  is  fixed  in  the  minds 
of  the  pupils,  it  is  quite  legitimate  to  use  that  as  a 
standard.  For  example,  in  describing  the  position  of 
the  British  forces  in  Natal  at  the  beginning  of  the  Boer 
War,  a  newspaper  correspondent  asked  his  readers  to 
treat  the  mountain  system  as  a  giant  letter  A,  with  the 
apex  pointing  north.  Then  he  proceeded  to  give  the 
position  of  Ladysmith  and  other  towns  within  the  letter, 
using  such  terms  as  the  bridge  of  the  A,  the  left  leg 
of  the  A,  the  enclosed  triangle  of  the  A.  These  figures 
have  a  compelling  power  that  directs  the  mind  of  the 
pupil,  whether  he  will  or  no. 

On  the  other  hand,  such  figures  must  be  very  definitely 
presented.  I  have  seen  considerable  confusion  arise 
in  a  junior  class  from  the  statement  that  the  watershed 
of  England  was  shaped  like  the  letter  T,  since  the 
teacher  had  to  explain  that  first  of  all  the  top  of  the  T 
was  not  quite  straight,  but  somewhat  squinted;  and 
further,  that  the  top  of  the  T  was  at  the  bottom  of  the 
map.  In  fact,  the  T  was  standing  on  its  head.  The 
same  illustration  succeeded  much  better  in  another  case, 
where  the  teacher  began  at  once  by  saying  that  the 
watershed  was  like  a  capital  T  turned  upside  down. 
The  minor  differences  were  introduced  when  the  pupils 
were  familiar  with  the  figure  as  a  whole. 


246    EXPOSITION   AND   ILLUSTRATION   IN  TEACHING 

It  often  happens  that  when  a  generalisation  has  been 
stated  the  pupil  understands  it  in  a  broad  way,  but  is 
not  quite  sure  as  to  its  application.  If  the  generalisa- 
tion is  followed  by  one  or  two  examples,  the  pupil  has 
the  opportunity  of  testing  how  far  his  impressions  are 
right.  Sometimes  the  examples  show  him  that  he  has 
taken  up  a  wrong  view  of  the  meaning  of  the  rule,  but 
even  when  he  has  not  to  change  his  first  view,  he  feels 
a  great  increase  in  confidence  from  having  seen  the 
rule  in  action.  A  capital  instance  of  such  a  useful  illus- 
tration is  to  be  found  in  the  continuation  of  a  passage 
quoted  from  Herbert  Spencer  in  Chapter  III  of  this 
book.  If  the  reader  will  turn  to  the  passage  referred  to 
and  reread  it,1  he  will  find  that  the  following  passage 
adds  considerably  to  the  clearness  of  the  otherwise  very 
satisfactory  exposition: — 

"Under  a  clear  sky,  and  with  no  trees,  hedges,  houses,  or  other 
objects  at  hand,  shadows  are  of  a  pure  blue.  During  a  red  sunset, 
mixture  of  the  yellow  light  from  the  upper  part  of  the  western  sky, 
with  the  blue  light  from  the  eastern  sky,  produces  green  shadows. 
Go  near  to  a  gas  lamp  on  a  moonlight  night,  and  a  pencil  placed  at 
right  angles  to  a  piece  of  paper  will  be  found  to  cast  a  purple  blue 
shadow  and  a  yellow  shadow,  produced  by  the  gas  and  the  moon 
respectively." 

It  is  now  easy  to  admit  what  was  suggested  at  the 
beginning  of  the  chapter,  that  even  when  we  are  dealing 
with  the  most  common  form  of  illustration,  the  supply- 
ing of  an  example  to  make  clear  the  application  of  a  rule, 
we  are  still  working  within  the  realms  of  analogy. 
The  example  owes  its  value  to  the  fact  that  it  is  in  at 
least  one  point  like  all  other  examples  of  the  principle 
it  exemplifies;  any  example  of  the  working  of  a  rule 

1  p.  76. 


EXEMPLIFICATION   AND   ANALOGY  247 

embodies  the  essential  relation  implied  in  that  rule, 
however  different  the  terms  between  which  the  relation 
exists. 

When  we  deal  with  the  type  as  illustration,  we  have  a 
special  case  of  the  illustration  of  the  rule  by  example. 
It  may  be  maintained  not  unreasonably  that  the  type 
really  combines  in  itself  the  rule  and  the  example: 
it  may  be  said  to  be  a  definition  become  concrete.  It 
corresponds  to  all  that  is  essential  in  the  rule.  Sup- 
pose we  are  dealing  with  insects,  for  instance;  any  in- 
sect will  serve  for  a  mere  example.  But  only  certain 
insects  possess  all  the  essential  elements  that  go  to 
the  formation  of  the  complete  connotation  of  "insect." 
No  insect  is,  as  a  matter  of  fact,  a  perfect  type  of  the 
class,  but  the  cockchafer  is  usually  selected  because 
he  combines  all  the  essential  qualities,  though  some  of 
them  are  present  only  in  a  rudimentary  form.  Some- 
times it  sounds  inappropriate  to  speak  of  a  type  at  all. 
Red  is  no  more  a  typical  colour  than  is  any  other.  It 
would  be  difficult  to  quote  a  typical  sentence.  "What 
is  nobler  than  to  die  for  one's  country?"  has  no  more 
right  to  be  regarded  as  a  type  than  has  the  homely 
"Cows  eat  grass."  But  when  we  come  to  special  kinds 
of  sentences,  —  exclamatory,  interrogative,  declaratory, 
—  we  may  well  have  a  type.  Having  defined  a  loose 
and  a  periodic  sentence,  it  is  quite  easy  to  select  a 
sentence  that  is  typically  loose,  and  another  that  is 
typically  periodic. 

In  dealing  with  the  type  it  is  well  to  make  it  as  ab- 
stract as  the  conditions  of  the  case  admit.  The  typi- 
cal insect  must  have  a  particular  colour,  since  we  cannot 
have  a  real  tangible  insect  without  colour  of  some  sort. 
But  of  this  colour  abstraction  should  be  made  in  ap- 


248    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

plying  our  type  as  illustration;  and  as  colour  is  one  of 
the  most  attractive  qualities,  we  may  find  this  abstrac- 
tion difficult.  On  the  other  hand,  in  dealing  with  the 
various  kinds  of  sentences,  we  find  it  easier  to  be 
abstract.  "That  a  is  b,  that  c  is  d,  that  e  is  f,  that  g  is 
h  cannot  be  questioned  "  is  a  typical  periodic  sentence. 
"He  denied  that  s  is  t,  that  u  is  v,  that  w  is  x,  that 
y  is  z"  is  an  equally  typical  loose  sentence.  The  ad- 
vantage of  expressing  them  in  this  abstract  form  is 
that  the  attention  is  directed  to  the  essential  point 
without  being  drawn  off  to  the  matter  which  might  be 
in  itself  interesting. 

While  the  type  as  illustration  should  be  made  as 
abstract  as  possible,  this  abstractness  should  not  be 
suddenly  introduced.  There  is  an  important  difference 
here  between  the  beginning  and  the  ending  of  a  process 
of  learning.  Illustrative  examples  at  the  beginning 
of  a  process  may  be  more  or  less  concrete,  with  proper 
precautions  against  their  monopolising  an  illegitimate 
amount  of  interest.  When  the  stage  of  the  particular 
has  been  mastered,  the  results  may  be  well  fixed  in  the 
pupil's  mind  in  its  barest  form  by  means  of  an  abstract 
type.  When  we  are  using  the  abstract,  at  any  rate,  it  is 
well  to  be  as  abstract  as  possible.  The  introduction  of 
a  little  of  the  concrete  in  the  middle  of  an  abstract 
formula  is  very  disconcerting.  This  cannot  be  better 
illustrated  than  by  reference  to  the  abstract  types  of  the 
periodic  and  loose  sentences  just  supplied  in  this  chapter. 
If  the  reader  remembers — and  very  probably  the  reader 
will  remember,  for  in  actual  teaching  the  point  has 
struck  quite  a  number  of  pupils — the  first  sentence  dealt 
with  the  first  letters  of  the  alphabet  and  the  second  with 
the  final  letters  of  the  alphabet.  The  pupil  at  once 


EXEMPLIFICATION  AND  ANALOGY  249 

wants  to  know  why.  He  is  so  accustomed  to  find  a 
meaning  in  all  the  illustrations  used,  and  to  find  a 
meaning  underlying  the  general  activities  of  life,  that 
he  very  naturally  looks  for  one  here.  He  applies  the 
principle  :  The  exception  proves  the  rule,  and  wants 
to  know  why  the  matter  —  for  in  this  case  the  bare 
letters  form  the  matter  —  should  be  different  in  the  two 
cases.1  Since  the  two  kinds  of  sentences  are  regarded 
as  differing  merely  in  form,  it  is  well  to  avoid  even  the 
trifling  difference  suggested  by  the  letters.  The  same 
letters  should  be  used  in  the  two  cases.  As  a  later 
exercise,  on  the  other  hand,  the  examples  might  be 
changed,  if  only  to  show  that  the  exact  number  of 
clauses  and  the  nature  of  the  subjects  and  predicates 
have  nothing  to  do  with  whether  a  sentence  is  periodic 
or  loose. 

1  It  is  because  of  this  that  in  changing  from  Murray's  Dictionary 
to  Webster's  in  Chapter  I  (p.  17)  I  have  taken  the  trouble  to  mention 
why.  Had  I  not  done  so,  I  should  certainly  have  been  asked  my 
reason  by  a  number  of  readers. 


CHAPTER  X 

THE  STORY  AS  ILLUSTRATION 

WHEN  the  worldly  wise  Chesterfield  gives  the  ad- 
vice, "Never  tell  stories,"  he  has  in  view  the  social 
bore.  He  is  pleading  for  the  rights  of  the  individual 
in  conversation,  which  are  always  endangered  when 
story-telling  creeps  in.  The  teller  of  tales  is  of  neces- 
sity a  monopolist. 

In  expository  work,  whether  hi  school  or  on  the  plat- 
form, the  speaker's  monopoly  is  already  granted,  so 
any  objection  to  story-telling  must  be  based  on  other 
grounds.  To  the  ordinary  listener  at  an  ordinary  les- 
son or  lecture,  even  a  comparatively  dull  story  is  more 
interesting  than  the  rest  of  the  talking,  and  need 
not,  if  the  expositor  has  the  necessary  skill,  interfere 
with  the  development  of  the  main  line  of  thought.  As 
a  matter  of  fact,  teaching  by  means  of  stories  is  of  the 
most  venerable  antiquity  and  is  practically  universal. 
Plato  recognises  its  importance  in  education.  In  The 
Republic l  we  have  the  following :  — 

"Socrates.  Shall  we  just  carelessly  allow  children  to  hear  any 
casual  tales  which  may  be  devised  by  casual  persons,  and  to  receive 
into  their  minds  ideas  for  the  most  part  the  very  opposite  of  those 
which  we  should  wish  them  to  have  when  they  are  grown  up  ? 

"  Adeimantus.   We  cannot. 

"Socrates.  Then  the  first  thing  will  be  to  establish  a  censorship 
of  the  writers  of  fiction,  and  let  the  censors  receive  any  tale  of  fiction 

1  Book  II,  Section  377;  the  English  is  Jowett's. 
250 


THE  STORY  AS  ILLUSTRATION  251 

which  is  good,  and  reject  the  bad ;  and  we  will  desire  mothers  and 
nurses  to  tell  their  children  the  authorised  ones  only.  Let  them 
fashion  the  mind  with  such  tales,  even  more  fondly  than  they  mould 
the  body  with  their  hands ;  but  most  of  those  which  are  now  in  use 
must  be  discarded." 

Plato  then  proceeds  to  give  examples  of  the  sort  of 
things  found  in  the  current  stories  of  his  time,  in  which 
the  gods  are  represented  as  doing  unworthy  things. 
Even  Homer  and  Hesiod  are  not  held  free  from  blame, 
and  would  require  a  great  deal  of  attention  from  the  cen- 
sor before  Plato  would  let  their  works  loose  among 
young  people.  Most  teachers  have  an  uncomfortable 
feeling  about  specially  prepared  "  books  for  the  young," 
and  it  is  with  a  little  shiver  that  they  approve  of  "the 
authorised  ones."  The  specially  prepared  story  is  apt 
to  suffer  from  the  dissipated  interest  of  the  author. 
He  has  to  keep  his  eye  so  closely  fixed  upon  the  censor 
that  he  is  apt  to  forget  the  children. 

We  shall  be  in  a  better  position  to  criticise  the  illus- 
trative story  when  we  have  considered  its  mode  of 
affecting  readers  or  hearers.  There  are  two  main  pur- 
poses to  be  served  by  the  story  as  a  means  of  instruc- 
tion, the  first  limited  to  the  communication  and  the 
acquirement  of  knowledge,  the  second  extending  to 
conduct.  In  the  second  class  there  are  two  divisions. 
For  in  using  the  story  as  a  means  of  affecting  conduct 
the  teacher  depends  upon  the  pupil's  inherent  tendency 
to  imitate,  and  according  as  this  imitation  is  direct  or 
mediated  by  some  degree  of  reflection  we  have  two 
forms  of  application,  primary  and  secondary.  There 
may  thus  be  said  to  be  in  all  three  outstanding  uses  of 
the  story. 

The  first  use  of  stories  is  to  give  practice  in  manipu- 


252    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

lating  ideas.  Terms  as  presented  to  us  in  text-books  are 
often  inert,  dead.  But  when  we  find  them  in  use  in  a 
story  they  are  living  and  functioning,  and  often  explain 
their  meaning  by  their  very  use  hi  a  context  that  is  other- 
wise intelligible.  We  find  them  there  as  we  find  them  in 
real  life.  In  fact,  story-reading  is  a  kind  of  living  at  the 
second  remove.  It  extends  and  enriches  our  experience. 
What  is  true  about  the  historical  novel  hi  the  teaching 
of  history  is  true  of  the  story  in  respect  of  life  in  general. 
It  shows  us  principles  in  action.  We  know  certain 
facts  as  facts  by  themselves,  but  in  the  story  we  find 
those  facts  applied  in  a  life  that  is  not  —  or  at  any  rate 
ought  not  to  be  —  very  different  from  our  own.  We 
seldom  realise  how  much  we  owe  to  stories  in  the  way 
of  education.  To  be  sure,  teachers  are  now  rather  keen 
on  the  subject  of  stories,  but  this  modern  interest  is 
only  the  coming  to  consciousness  of  a  principle  that  has 
been  long  applied.  We  are  becoming  conscious  of  and 
are  writing  about  the  educative  influence  of  the  old 
story-tellers,  wandering  minstrels,  peddlers,  and  fireside 
Scheherazades;  but  then*  influence  has  been  present 
all  the  while.  The  use  of  the  story  that  we  are  at 
present  considering  is  independent  of  the  moral  effect 
of  any  deliberate  lesson  the  story  may  convey.  The 
value  lies  hi  the  material  presented  to  the  mind  for 
exercise. 

Consistency  with  the  facts  of  ordinary  life  is  surely 
a'modest  demand  to  make  from  the  user  of  illustrative 
stories.  The  moral  may  be  unimpeachable,  and  the 
rarer  condition  of  truth  to  human  nature  may  be  ob- 
served, but  if  a  glaring  breach  of  natural  law  is  detected 
in  a  story,  all  the  rest  goes  for  nothing :  harm  is  done, 
not  good.  The  classical  story  of  the  magnanimous 


THE  STORY  AS  ILLUSTRATION  253 

miner  is  a  case  in  point.  The  vessel  is  slowly  settling  in 
mid-ocean.  The  miner  who  is  returning  after  having 
made  his  pile  has  completed  the  arrangements  necessary 
to  meet  the  catastrophe.  The  confiding  little  girl,  who 
of  course  has  no  relatives  on  board,  comes  up,  and  in 
good  Sunday-school  language  says,  "Oh,  sir,  can  you 
swim  ?"  He  admits  that  he  can,  so  she  at  once  places 
herself  under  his  protection,  and  so  touched  is  he  with 
her  implicit  faith  [see  alphabetical  index]  that  he  at 
once,  though  of  course  reluctantly,  removes  the  belt  that 
contains  his  gold  —  worth  two  and  a  half  million  —  and 
does  what  is  right  [see  under  Duty  in  the  alphabetical 
index,  for  the  story  appears  under  this  head  as  well]. 
As  a  rule  the  attention  is  so  much  taken  up  with  the 
moral  side  of  the  question  that  no  trouble  arises.  But 
if  anyone  happens  to  take  up  the  "arithmetical  chal- 
lenge" implied  in  the  $2,500,000,  and  works  out  the 
actual  weight  of  this  value  of  gold,  the  anecdote  suffers 
serious  moral  damage.  The  weight  of  gold  the  poor 
fellow  is  represented  as  carrying  in  his  belt  weighs  some 
trifle  more  than  four  tons.  The  pity  is  that  the  whole 
story  goes  to  pieces  on  this  fact,  for  $25,000  would 
have  served  the  illustrator's  purpose  just  as  well.  The 
smaller  sum  would  weigh  about  91  pounds,  quite  a 
sufficient  handicap  to  prevent  the  miner  trying  to  save 
both  the  girl  and  the  belt. 

The  second  and  most  obvious  use  of  the  story  is  to 
incite  to  a  definite  line  of  action.  "Go  thou  and  do 
likewise"  is  the  natural  ending  to  stories  of  this  kind. 
It  is  clear  that  Plato  has  this  imitative  use  mainly  in 
view.  The  doings  of  Uranus  and  Cronos  are  not  to  be 
told  to  the  boy,  lest  in  later  years  he  should  make  a 
practical  application  of  what  he  had  learned  and  — 


254    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

"even  if  he  chastises  his  father  when  he  does  wrong,  in  whatever 
manner,  he  will  only  be  following  the  example  of  the  first  and  great- 
est among  the  gods." l 

Plato  is  no  believer  in  the  awful  example ;  he  knows  that 
the  suggestive  force  of  imitation  works  in  one  direction 
only.  This  class  of  story,  then,  should  be  as  straightfor- 
ward as  possible.  Parallelism  should  be  avoided  where 
direct  teaching  is  available,  and  when  used  should  be 
made  as  clear  as  possible,  and  as  free  from  refinements. 
Such  stories  are  illustrative  of  life,  and  should  bear  the 
test  of  constant  comparison  with  things  as  they  are. 
School  stories  are  apt  to  fall  lamentably  short  here. 
The  classical  sinner  in  this  respect,  if  we  are  to  believe 
the  popular  clamour  among  teachers,  is  Eric,  or  Little  by 
Little.  Priggishness  is  the  universal  complaint  against 
books  of  this  class,  and  it  is  perhaps  impossible  to  avoid 
this  vice  when  we  set  ourselves  deliberately  to  prepare 
an  illustrative  story.  But  the  priggishness  in  moral 
school  stories  is  trifling  compared  with  the  unnaturalness 
introduced  into  the  Sunday-school  story  of  commercial 
success.  In  business,  if  anywhere,  it  is  easy  to  test 
recipes  for  success.  A  boy  who  is  brought  up  on  stories 
of  the  immediate  commercial  success  that  follows  upon 
religious  practice  is  apt  to  become  unduly  depressed 
when  he  enters  on  real  life.  In  the  book  the  young 
man  is  dismissed  because  he  has  lost  an  order  by  con- 
fessing that  the  beans  were  not  of  the  same  quality  at 
the  bottom  of  the  barrel.  This  is  true  to  life.  But  the 
book2  makes  the  employers  write  to  the  young  man  a 
few  days  later,  saying  they  had  a  position  of  great 
trust  vacant,  and  would  he  accept  it  at  $300  increase 

1  Republic,  II,  378. 

1  Bible  Models,  by  Dr.  Richard  Newton,  p.  57. 


THE   STORY  AS  ILLUSTRATION  255 

on  his  former  salary.  This  is  not  quite  close  to  the 
facts  of  business  life.  What  could  be  more  misleading 
than  the  following,  a  type  of  hundreds  of  illustrative 
stories :  — 

"  A  few  years  ago  the  owner  of  a  large  drug-store  advertised  for 
a  boy.  The  next  day  the  store  was  thronged  with  boys  applying 
for  the  place.  Among  them  was  a  queer-looking  little  fellow,  accom- 
panied by  his  aunt.  '  Can't  take  him,'  said  the  gentleman ;  ' he's  too 
small.' 

"  '  I  know  he's  small,'  said  the  aunt,  'but  he's  prompt  and  faithful.' 

"  After  some  consultation  the  boy  was  set  to  work.  [Naturally 
employers  would  take  the  smallest  of  the  throng,  if  only  he  had  an 
aunt  with  him.]  Not  long  after,  a  call  was  made  on  the  boys  for 
someone  to  stay  in  the  store  all  night.  The  other  boys  seemed 
reluctant  to  offer  their  services.  But  this  boy  promptly  said, 'I'll 
stay,  sir.' 

"  In  the  middle  of  the  night  the  merchant  went  into  the  store  to 
see  that  all  was  right,  and  found  the  boy  busy  at  work  cutting  labels. 
'What  are  you  doing,  my  boy  ? '  said  he.  ' I  didn't  tell  you  to  work 
all  night.' 

"  'I  know  you  didn't,  sir,  but  I  thought  I  might  as  well  be  doing 
something.' 

"The  next  day  the  cashier  was  told  to  'double  that  boy's  wages, 
for  he  is  prompt  and  industrious.' 

"  Not  many  weeks  after  this,  a  show  of  wild  beasts  was  passing 
through  the  streets,  and  naturally  enough  all  the  hands  in  the  store 
rushed  out  to  see  them.  A  thief  saw  his  opportunity,  and  entered  by 
the  back  door  to  steal  something.  But  this  prompt  boy  had  stayed 
behind.  He  seized  the  thief,  and  after  a  short  struggle  captured 
him.  [Do  not  forget  how  small  he  was  awhile  ago  —  but  then, 
maybe  it  was  a  small  thief.]  Not  only  was  a  robbery  prevented,  but 
valuable  articles  stolen  from  other  stores  were  recovered. 

"  'Why  did  you  stay  behind,'  asked  the  merchant  of  this  boy, 
'when  all  the  others  went  out  to  see  the  show?' 

"  '  Because,  sir,  you  told  me  never  to  leave  the  store  when  the 
others  were  absent ;  so  I  thought  I'd  stay.' 

"  Orders  were  given  once  more :  '  Double  that  boy's  wages,  for  he 
is  not  only  prompt  and  industrious,  but  faithful.'  [How  soon  one 


256    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

acquires  the  doubling  habit !]  That  boy  is  now  getting  a  salary  of 
twenty-five  hundred  dollars  a  year,  and  before  long  he  will  become  a 
member  of  the  firm.  [We  are  a  little  surprised  at  the  delay  in  mak- 
ing him  a  partner.]  He  was  following  Elijah's  model  of  promptness, 
and  it  helped  to  make  his  fortune."  ' 

What  a  disillusionment  is  in  store  for  boys  brought 
up  on  such  travesties  of  real  life! 

The  third  use  of  the  story  as  Illustration  resembles  the 
second  inasmuch  as  it  conveys  a  direct  lesson,  but  differs 
from  it  since  it  does  not  present  a  simple  line  of  conduct 
to  be  imitated.  It  rather  suggests  general  principles 
which  must  be  applied  by  the  pupil  to  his  own  case. 
Sometimes  it  is  written  to  order,  as  hi  the  case  of  fables 
and  allegories,  but  sometimes  it  has  been  made  for  quite 
other  purposes  and  has  had  a  meaning  read  into  it  by 
some  ingenious  expositor.  New  applications  of  famil- 
iar old  stories  illustrate  this  use.  A  great  many  of  our 
political  cartoons  are  based  on  this  manipulation  of 
old  material  in  a  new  connection.  An  ingenious  com- 
mentator illustrated  his  whimsical  view  of  what  he 
called  "The  Devil's  Apprenticeship"  by  showing  the 
gradual  improvement  in  temptation  methods,  as  shown 
by  three  historical  examples  of  Satan's  workmanship. 
In  the  case  of  Job  he  knew  so  little  about  his  business 
that  he  endeavoured  to  obtain  his  ends  by  blundering 
brutality  and  cruelty.  When  it  came  to  the  temptation 
of  Our  Lord  he  had  learnt  enough  to  go  about  the 
matter  in  quite  a  different  way;  and  had  he  had  to  deal 
with  an  ordinary  case  he  would  probably  have  won, 
thanks  to  his  more  attractive  methods.  But  when  the 
turn  of  Faust  came,  Satan  had  learned  his  art  of  tempta- 
tion so  well  that  he  was  irresistible.  He  had  learned  not 

1  Dr.  Richard  Newton :  Bible  Models,  p.  179. 


THE  STORY  AS  ILLUSTRATION  257 

to  bully  and  torture;  he  had  given  up  even  the  attrac- 
tive lure;  he  did  not  pester  Faust  one  way  or  the  other: 
he  waited  till  he  was  called.  Had  the  commentator 
known  of  the  newer  psychology,  he  might  have  expressed 
his  meaning  by  saying  that  Satan  had  attained  the 
point  of  carrying  on  temptation  by  means  of  pseudo- 
auto-suggestion. 

Nowhere  can  we  find  a  better  example  of  what  Plato 
would  call  "authorised  tales"  than  in  the  Fables  of  La 
Fontaine.  These  were,  and  to  some  extent  still  are, 
recognised  as  specially  suitable  for  the  instruction  of 
the  young.  They  held  the  place  hi  France  that  the 
Catechism  held  in  Scotland.  Children  were  asked  if 
they  knew  their  fables  just  as  a  teacher  might  ask  a  boy 
if  he  knew  "his  tables,"  or  as  Roger  Ascham  might  have 
asked  him  if  he  knew  "his  noun."  It  was  only  there- 
fore to  be  expected  that  Rousseau  would  have  something 
very  serious  to  say  against  them.  His  attack  in  the 
Emile  1  follows  two  different  lines,  the  cognitive  and  the 
moral.  The  first  part  of  his  criticism  deals  with  the 
matter  of  the  fables  mainly  from  the  point  of  view  of 
the  children's  intelligence.  He  is  anxious  to  show,  in  the 
first  place,  that  children  cannot  understand  the  fables. 
When  he  has  demonstrated  this  to  his  satisfaction,  he 
proceeds  to  show  that  even  if  they  did  understand,  they 
would  be  sure  to  misapply  their  knowledge.  The  first 
part,  therefore,  deals  with  the  expository  side,  the  second 
more  directly  with  the  illustrative.  As  both  are  of  the 
greatest  interest  in  connection  with  our  subject,  the 
passage  is  worth  quoting  in  its  entirety.  Since  the  Rous- 
seau criticism  demands  a  line-for-line  translation  of  the 
fable  of  the  Fox  and  the  Crow,  I  have  been  driven, 

1  Edition  de  Ch.  Lahure,  1856,  Livre  II,  p.  490  ff. 
a 


258    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

though  not  even  on  speaking  terms  with  the  Muses,  to 
make  a  rendering  of  my  own. 

THE  FOX  AND  THE  CROW 

On  tree-top  perched  sat  Master  Crow : 

Within  his  beak  he  held  a  cheese, 
The  scent  led  Master  Fox  below, 

Who  him  addressed  in  words  like  these : 
"Ha !  good  day,  good  day,  dear  Sir  Crow; 
How  fair  you  are !    How  do  your  looks  me  please ! 

Without  a  lie,  if  but  your  note 

Matches  at  all  your  beauteous  coat, 
You  are  the  phenix  'mongst  the  woodland  train." 

These  words  with  joy  nigh  turned  the  crow's  weak  brain : 

And  to  display  his  dulcet  strain 
He  opes  his  beak  —  down  falls  the  cheese  amain. 
The  fox  enjoyed  the  cheese,  then  said,  "  Good  Sir : 

Now  learn  that  every  flatterer 

Lives  upon  him  his  flatt'ries  please : 
A  lesson  this  no  doubt  well  worth  a  cheese." 

Confounded  and  ashamed,  the  crow 
Swore,  somewhat  late,  none  else  should  have  him  so. 

CRITICISM  BY  ROUSSEAU 

On  tree-top  perched  sat  Master  Crow  : 

"Master."  What  is  the  meaning  of  this  word  in  itself?  What 
does  it  mean  before  a  proper  name  ?  What  meaning  has  it  here  ? 

What  is  a  crow  ? 

What  is  the  meaning  of  "  on  tree-top  perched  "  ?  We  do  not  say 
"  on  tree-top  perched,"  but  "  perched  on  a  tree-top."  Consequently 
we  must  speak  of  poetical  inversions.  We  must  tell  what  prose  is 
and  verse. 

Within  his  beak  he  held  a  cheese, 

What  cheese  ?  Was  it  Swiss,  Brie,  or  Dutch  ?  If  the  child  has 
never  seen  a  crow,  what  do  you  gain  by  speaking  to  him  of  it  ?  If 


THE  STORY  AS  ILLUSTRATION  259 

he  has  seen  one,  how  can  he  imagine  it  holding  a  cheese  in  its  beak  ? 
Let  us  always  make  our  illustrations  agree  with  nature. 

The  scent  led  Master  Fox  below, 

Another  "Master."  But  this  time  by  good  right.  He  is  past 
Master  in  all  the  tricks  of  his  trade.  We  must  tell  what  a  fox  is, 
and  distinguish  his  true  nature  from  the  conventional  character 
which  he  has  in  fables. 

Led  by  the  scent  of  a  cheese 

This  cheese,  held  by  a  crow  perched  upon  a  tree-top,  must  have 
had  a  powerful  smell  to  be  perceived  by  the  fox  in  a  thicket  or  in  a 
burrow.  Is  it  thus  that  you  exercise  your  pupil  in  the  spirit  of 
well-balanced  criticism  which  only  allows  itself  to  be  imposed  upon 
under  suitable  artistic  conditions,  and  can  discriminate  between 
truth  and  lying  in  the  tales  of  another  ? 

Who  him  addressed  in  words  like  these  : 

Words  !  Foxes  speak,  then  ?  They  speak  the  same  language  as 
crows !  Wise  instructor,  be  careful.  Weigh  well  your  reply  before 
making  it :  it  means  more  than  you  think. 

"Ha  !  good  day,  good  day,  dear  Sir  Crow; 

Sir  !  A  title  which  the  child  sees  turned  into  ridicule,  even  before 
he  knows  that  it  is  a  title  of  honour.  Those  who  say  Sir  Crow  will 
have  plenty  to  do  before  they  explain  this  Sir. 

How  fair  you  are  !     How  do  your  looks  me  please  ! 

Padding,  useless  repetition.  The  child,  seeing  the  same  thing 
repeated  in  different  terms,  learns  to  speak  slovenly.  If  you  say 
that  this  redundancy  is  an  art  of  the  author,  that  it  enters  into  the 
plan  of  the  fox,  who  wants  to  appear  to  multiply  praises  with  words, 
that  excuse  will  do  for  me,  but  not  for  my  pupil. 

Without  a  lie,  if  but  your  note 

Without  a  lie!  People  lie,  then,  sometimes.  What  can  the 
child  think  if  you  explain  to  him  that  the  fox  only  said  "without  a 
lie  "  because  he  was  lying. 


260    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

Matches  at  all  your  beauteous  coat, 

Matches  !  What  does  this  word  mean  ?  Teach  the  child  to  com- 
pare things  so  different  as  voice  and  plumage :  you  will  see  how  he 
will  understand  you. 

You  are  the  phenix  'mongst  the  woodland  train." 

The  phenix  !  What  is  a  phenix  ?  Here  we  are  all  at  once  thrown 
into  the  fictions  of  antiquity,  almost  into  mythology. 

The  woodland  train !  What  figurative  speech !  The  flatterer 
ennobles  his  speech  and  gives  it  more  dignity  in  order  to  render  it 
more  seductive.  Will  a  child  understand  this  delicate  policy  ?  Does 
he  ever  know,  can  he  know,  what  a  noble  or  a  low  style  is  ? 

These  words  with  joy  nigh  turned  the  crow's  weak  brain  : 

One  must  have  already  experienced  very  keen  passions  to  under- 
stand this  proverbial  expression. 

And  to  display  his  dulcet  strain 

Do  not  forget  that  to  understand  this  verse,  and  all  the  fable, 
the  child  must  know  what  the  dulcet  strains  of  a  crow  are. 

He  opes  his  beak  —  downfalls  the  cheese  amain. 

This  line  is  admirable.  »The  very  harmony  makes  a  picture  of  it. 
I  see  a  big  ugly  open  beak;  I  hear  the  cheese  falling  through  the 
branches ;  but  beauties  like  these  are  lost  on  children. 

Opes.1  This  word  is  out  of  ordinary  use.  It  must  be  explained. 
One  must  say  that  it  is  only  used  in  verse.  The  child  will  ask  why 
people  speak  differently  in  prose  and  in  verse.  What  will  you  answer 
him? 

The  fox  enjoyed  the  cheese,  then  said  "Good  Sir : 

Here  we  have,  then,  already,  goodness  turned  into  vileness. 
Certainly  the  tree  of  knowledge  is  an  early  plant  in  our  children's 
garden. 

1  In  the  original  this  note  applies  to  the  word  allecht  in  the  third 
line  from  the  beginning,  but  the  general  sense  is  not  at  all  changed 
by  transferring  the  remarks  to  the  English  poetical  form,  opes. 


THE  STORY  AS  ILLUSTRATION  261 

Now  learn  that  every  flatterer 
General  statement ;  we  are  quite  beyond  our  depth. 

Lives  upon  him  his  flatt'ries  please: 
No  child  of  ten  will  ever  understand  this  line. 

A  lesson  this  no  doubt  well  worth  a  cheese." 

That  is  true,  and  the  thought  is  very  good.  Yet  there  will  be 
found  very  few  children  who  can  compare  a  lesson  to  a  cheese,  and 
who  would  not  prefer  the  cheese  to  the  lesson.  We  must  get  them  to 
understand,  then,  that  this  remark  is  only  a  joke.  What  fine-drawn 
distinctions  for  children ! 

Confounded  and  ashamed,  the  crow 
Another  pleonasm;  but  this  one  is  unpardonable. 

Swore,  somewhat  late,  none  else  should  have  him  so. 

Swore!  What  sort  of  blockhead  is  the  master  who  dares  to 
explain  to  a  child  what  an  oath  is  ? 

Here  we  have  abundance  of  details,  yet  not  so  many  as  would  be 
necessary  to  analyse  all  the  ideas  of  this  fable,  and  to  reduce  them 
to  the  simple  and  elementary  ideas  of  which  each  of  them  is  com- 
posed. But  who  believes  that  there  is  need  of  this  analysis  to  make 
oneself  understood  by  the  young?  None  of  us  is  philosopher 
enough  to  put  himself  in  the  place  of  a  child. 

Now  all  this  is  ingenious,  and  very  effectively  put. 
Unfortunately,  it  does  not  stand  the  test  of  practical 
application.  Rousseau  has  fallen  into  the  very  common 
mistake  of  underestimating  the  intelligence  of  a  child. 
Further,  he  has  made  the  mistake  of  specifying  an  age. 
Most  of  us  would  have  thought  his  criticisms  applied  to 
a  child  of  seven.1  We  find  that  he  has  in  view  a  child  of 
ten.  One  of  the  teacher's  chief  difficulties  with  children 

1  In  his  criticism  of  the  moral  he  speaks  of  "  children  of  six." 


262    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

of  this  age  is  to  keep  them  from  generalising  too  freely. 
Not  only  do  children  of  ten  easily  understand  the 
generalisation,  "every  flatterer  lives  upon  him  his 
flatt'ries  please,"  but,  unfortunately,  many  of  them 
actually  apply  it.  There  is  no  difficulty  whatever  in 
getting  a  class  of  pupils-  of  ten  to  understand  this 
fable.  As  a  matter  of  fact,  the  teacher  of  such  a 
class  will  have  to  face  a  certain  resentment  among  the 
pupils  at  having  to  deal  with  such  childish  matters. 
As  to  the  special  difficulties  raised  by  Rousseau,  they 
can  be  all  easily  overcome  or  postponed.  It  is  not  at  all 
necessary,  for  example,  that  there  should  be  an  elabo- 
rate discussion  of  the  nature  of  prose  and  verse.  Chil- 
dren of  ten  know  exceedingly  well  in  a  practical  way 
what  each  is,  and  the  time  for  a  logical  definition  is  not 
yet.  Would  anyone  maintain  that  such  a  definition  is 
necessary  before  a  child  can  understand  fully  the  fable 
before  him  ?  The  inversion  that  distresses  Rousseau 
will  certainly  be  noted  by  the  pupil.  He  will  feel  that  it 
is  different  from  the  rest  of  his  book  work,  just  as  he 
notes  that  much  of  his  book  work  is  different  from  his 
spoken  work.  He  is  becoming  practically  acquainted 
with  what  inversion  means;  he  is  laying  up  a  capital  of 
experience  of  literary  form  against  the  day  when  he  has 
to  face  the  ordinary  laws  of  rhetoric.  The  enquiry 
about  the  kind  of  cheese  is  puerile.  The  dilemma  about 
seeing  a  crow  is  avoided  by  showing  a  picture  —  which, 
by  the  way,  settles  the  relative  size  of  the  cheese  at  the 
same  tune.  Rousseau  and  the  naturalists  may  be  left 
to  fight  it  out  about  the  fox's  sense  of  smell.  Grown-up 
people  hear  enough  about  the  wonderful  powers  of 
animals  in  this  way  to  be  willing  to  accept  La  Fontaine 
at  his  face  value,  and  children  will  certainly  not  suffer 


THE  STORY  AS  ILLUSTRATION  263 

from  following  their  example.  As  to  the  conventional 
character  of  the  fox,  there  is  not  much  that  the  child  of 
ten  brought  up  on  ordinary  schoolbooks  does  not  know. 
The  idea  of  a  child  learning  to  speak  slovenly  from 
imitating  the  style  of  La  Fontaine  ! 

" People  lie,  then,  sometimes."  The  naif  Rousseau 
would  have  us  believe  that  a  child  of  ten  is  not  aware  of 
this.  Even  an  English  judge  would  not  dare  to  claim 
such  ignorance.  "Matches"  would  give  very  little  dif- 
ficulty to  a  class  of  girls,  and  no  class  of  boys  of  ten 
could  be  puzzled  by  the  recondite  statement,  "If 
your  singing  is  as  fine  as  your  coat  is  pretty."  Phenix 
must,  of  course,  be  explained ;  that  is,  we  must  tell  the 
child  what  we  have  read  in  books  about  it.  In  two 
minutes  the  child  knows  as  much  about  it  as  most  of  us 
go  through  life  with.  "Can  a  child  know  what  a  noble 
and  a  low  style  is?"  Certainly,  if  only  Rousseau  will 
allow  him  to  have  examples  of  the  noble  style.  The 
other  he  usually  has  thrust  upon  him.  Does  anyone 
think  that  a  child  of  ten  cannot  discriminate  between 
the  style  of  a  comic  song  and  that  of  Hiawatha  or  one 
of  Macaulay's  Lays.  Naturally  the  child  cannot  write 
a  thesis  on  the  distinction.  "Turned  the  crow's  weak 
brain"  seems  to  Rousseau  a  terrible  strain  on  the  chil- 
dren's intelligence.  The  trouble  is  that  for  this  expres- 
sion the  pupils  I  have  tested  have  usually  had  too  many 
equivalents.  Unfortunately,  they  were  rather  of  the 
"low  style":  —  "got  barmy  with  joy,"  "off  his  nut 
with  joy,"  "so  glad  he  got  a  slate  loose";  not  elegant, 
but  horribly  expressive  of  full  comprehension. 

While  on  the  score  of  intelligence  Rousseau  is  over- 
anxious, and  certainly  overcritical,  he  has  a  strong 
case  when  he  takes  up  the  moral  aspect:  — 


264    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

"  I  ask  if  it  is  to  children  of  six  that  we  should  teach  that  there  are 
men  who  flatter  and  lie  for  their  profit  ?  One  might  at  most  teach 
them  that  there  are  mockers  who  make  fun  of  little  boys,  and  laugh 
in  their  sleeves  at  silly,  boyish  vanity ;  but  the  cheese  spoils  every- 
thing ;  one  teaches  them  not  so  much  to  drop  the  cheese  from  their 
own  mouths  as  to  make  it  drop  from  the  mouth  of  another.  Here, 
then,  is  my  second  paradox,  and  it  is  not  the  least  important. 

"  Observe  children  learning  their  fables,  and  you  will  see  that  when 
they  are  in  a  position  to  apply  them  they  almost  always  do  it  in  a 
way  contrary  to  the  intention  of  the  author ;  and  that  instead  of 
guarding  themselves  against  the  vice  of  which  we  wish  to  cure  or  from 
which  we  wish  to  protect  them,  they  are  inclined  to  love  the  vice  by 
means  of  which  one  makes  profit  out  of  the  failings  of  others.  In  the 
preceding  fable  children  laugh  at  the  crow,  but  they  have  all  a  warm 
side  towards  the  fox ;  in  the  following  fable  you  think  you  are  giving 
them  the  grasshopper  as  an  example  —  not  at  all,  it  is  the  ant  that 
they  will  choose.  One  does  not  like  to  eat  humble  pie :  they  will 
always  play  the  grand  part;  it  is  the  choice  of  self-love,  a  most 
natural  choice.  But  what  a  ghastly  lesson  for  children  !  The  most 
hateful  of  all  monsters  would  be  a  hard  and  miserly  child,  knowing 
what  was  asked  of  him,  yet  refusing.  The  ant  does  more :  she 
teaches  the  child  to  chaff  while  refusing. 

"  In  all  the  fables  where  the  lion  is  one  of  the  characters,  since 
he  is  the  most  distinguished,  the  child  never  fails  to  make  himself 
the  lion;  and  when  he  superintends  distribution,  well  taught  by 
his  model,  he  is  most  careful  to  seize  everything.  But  when  the 
gnat  gets  the  better  of  the  lion,  that  is  another  affair:  then  the 
child  is  no  longer  the  lion,  he  is  the  gnat.  He  learns  to  kill  one 
day  by  needle-thrusts  those  whom  he  dare  not  attack  in  a  stand- 
up  fight. 

"  In  the  fable  of  the  lean  wolf  and  the  fat  dog  in  place  of  the  lesson 
in  moderation  which  is  intended  to  be  conveyed,  he  takes  a  lesson  in 
licence.  I  shall  never  forget  seeing  a  little  girl  weep  copiously 
because  she  was  being  taught  docility  by  means  of  this  fable.  Her 
friends  could  not  understand  the  cause  of  her  tears ;  at  length  they 
learned.  She  felt  galled  like  the  dog ;  she  wept  because  she  was  not 
the  wolf. 

"Thus,  then,  the  moral  of  the  first  fable  quoted,  is  for  the  child  a 
lesson  in  the  basest  flattery ;  that  of  the  second  a  lesson  in  inhuman- 


THE  STORY  AS  ILLUSTRATION  265 

ity;   that  of  the  third  a  lesson  in  injustice;  that  of  the  fourth  a 
lesson  in  satire ;  that  of  the  fifth  a  lesson  in  self-sufficiency. 


"  But  perhaps  all  this  moral  which  serves  me  as  an  objection 
against  fables  may  furnish  so  many  reasons  for  preserving  them. 
We  must  have  one  moral  in  words  and  another  in  actions  in  society, 
and  these  two  do  not  at  all  resemble  each  other.  The  one  is  in  the 
Catechism,  where  folks  leave  it;  the  other  is  in  the  fables  of  La 
Fontaine." 

Depressing  as  all  this  sounds,  it  is  not  without  its 
bright  side.  The  very  self-reference  that  Rousseau 
deplores  is  in  itself  a  force  that  can  be  utilised  by  the 
teacher.  It  has  to  be  remembered  that,  however  this 
self-reference  may  be  debased  by  the  love  of  the  lime- 
light, it  is  in  itself  an  essential  part  of  our  nature. 
From  what  we  have  seen  already  as  to  the  nature  of 
consciousness,  we  are  compelled  to  regard  everything 
from  our  ovm  point  of  view.  Whether  we  will  or  no, 
we  must  treat  subjects  on  the  assumption  that  we  are  at 
the  centre  of  the  universe.  Not  conceit  but  necessity 
makes  us  treat  ourselves  as  the  centre  of  all  things. 

As  for  the  desire  for  the  best  part  in  the  drama  of  life, 
that  also  is  natural,  but  must  be  regulated  by  the  possi- 
bilities of  the  case.  Experience  must  teach  the  child 
his  true  place  in  the  play,  and  the  least  costly  experience 
is  that  of  the  second  remove,  as  supplied  by  stories. 
Knowing  that  the  pupil  will  inevitably  put  himself 
among  the  dramatis  personce  of  the  story,  and  almost 
inevitably  cast  himself  for  the  hero's  part,  the  teacher 
knows  how  to  arrange  his  material.  To  begin  with, 
the  knowledge  of  this  self-referent  tendency  frees  the 
teacher  from  the  necessity  for  that  blatant  moralising 
that  most  of  us  dislike.  This  does  not  mean  that  the 


266    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

teacher  is  not  to  take  direct  means  to  affect  the  pupil, 
but  merely  that  he  need  not  expound  his  methods  and 
aims.  If  he  arranges  his  materials  properly,  the  pupil 
will  inevitably  do  the  rest.  The  story  must  be  so  pre- 
sented as  to  convey  a  clear  lesson;  the  pupils  must  be 
left  to  draw  the  moral  for  themselves.  In  cases  where 
there  is  a  conflict  of  opinion,  there  is  room  for  exposition 
and  even  exhortation.  But  when  the  story  raises  a  clear 
issue,  the  pupils  may  well  be  left  to  settle  the  matter  for 
themselves. 

A  very  effective  example  of  the  sort  of  self-interpret- 
ing story  is  to  be  found  in  the  anecdote  laid  before  a 
mixed  class  of  boys  and  girls  in  one  of  the  slum  schools  of 
London.  There  was  no  comment  made  by  the  teacher 
at  the  time,  and  it  would  almost  appear  as  if  even  the 
circumstances  under  which  the  story  was  told  in  school 
might  be  left  to  be  inferred  from  the  story  itself:  — 

"  Solomon  did  many  other  clever  things  besides  finding  out  who 
was  the  true  mother  of  the  living  child.  When  the  Queen  of  Sheba 
came  to  see  him,  she  gave  him  a  great  many  puzzling  things  to  do, 
but  he  did  them  all,  and  was  never  once  caught  out.  One  of  her 
most  cunning  puzzles  was  to  bring  to  him  a  dozen  children,  all 
dressed  exactly  alike,  with  their  hair  just  the  same  length  and 
combed  in  the  same  way.  Some  of  them  were  boys  and  some  girls ; 
and  the  puzzle  was  for  Solomon  to  say  which  were  which.  All  he 
did  was  to  order  his  servants  to  bring  basins  and  make  all  the 
children  wash  their  hands.  When  this  was  finished,  he  picked 
out  those  who  had  washed  their  hands  only,  but  not  the  wrists, 
and  said  these  were  the  boys.  And  he  was  right."  * 

Unfortunately,  certain  stories  are  so  ill  adapted  for 
their  purpose  that  the  pupil  is  not  only  left  in  doubt, 

1  It  goes  without  saying  that  my  approval  of  the  illustrative  effi- 
ciency of  this  story  does  not  carry  with  it  approval  of  fabrication  of 
Scripture  incidents. 


THE   STORY   AS   ILLUSTRATION  267 

but  actually  impelled  to  draw  a  totally  wrong  moral. 
Take  the  following  story,  intended  to  illustrate  living 
faith :  — 

"At  the  Battle  of  Waterloo,  Nathan  Meyer  Rothschild  was  in  a 
shot-proof  tent,  with  a  swift  horse  saddled  and  bridled  by  his  side. 
At  sunset  he  peered  over  the  battlefield,  and  saw  our  soldiers 
sweeping  the  French  before  them.  'Hurrah !'  he  cried,  'the  house 
of  Rothschild  has  won  Waterloo ' :  his  house  had  lent  the  money  for 
it.  He  sprang  into  the  saddle,  galloped  all  night,  reached  the 
shore  at  daybreak,  bribed  a  fisherman  to  take  him  across  the  stormy 
sea,  and  by  whipping  and  spurring,  reached  London  thirty-six  hours 
before  anyone  else.  He  used  these  hours  in  buying  up  all  the 
stocks  he  could,  and  gained  nearly  two  millions  of  pounds.  Many  on 
the  battlefield  besides  him  had  perfect  faith  in  the  good  news,  but 
their  faith  was  a  thin,  lazy  thing,  and  did  not  rouse  them  to  act  at 
once.  And  so  a  faith  that  does  not  master  and  move  you  cannot 
make  you  rich  in  the  goods  of  the  soul.  Real  Christianity  is  a  real 
living  faith  in  a  real  living  Saviour:  it  is  a  whole  faith  in  a  whole 
Saviour." ' 

This  story  has  clearly  lost  its  way.  It  has  strayed  out 
of  some  "How  to  Succeed"  series,  where  it  was  com- 
fortably at  home.  What  has  this  shot-proof  stock- 
broker to  do  with  the  real  Christianity  of  the  conclud- 
ing sentence  ?  What  can  the  boy  learn  from  this  story 
but  to  despise  the  soldiers  whose  thin,  lazy  faith  did  not 
rouse  them  to  act  at  once,  and  make  a  dash  for  London 
to  scramble  for  their  share  of  those  two  millions  of 
pounds !  In  a  case  like  this  a  moral  is  needed,  as  no  one 
would  suspect  the  author's  meaning  without  it.  But  a 
story  that  really  illustrates  does  not  require  a  formal 
moral  at  the  end.  On  the  other  hand,  it  is  not  unneces- 
sary to  remark  that  there  is  nothing  really  disgraceful 
in  using  a  moral.  So  strong  is  the  objection  some  people 

1  Bible  Object  Lessons,  James  Nesbit  &  Co.,  London,  1891,  p.  71. 


268    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

have  to  this  form  of  direct  moral  instruction  that  they 
would  almost  have  us  believe  that  there  is  something 
morally  wrong  in  definitely  proclaiming  moral  truth. 
The  expression  or  suppression  of  the  moral  is  a  matter  of 
psychology,  not  of  ethics.  There  is  no  ethical  objection 
to  our  urging  people  to  be  moral.  The  only  objection 
that  is  valid  is  that  we  may  be  less  able  to  gain  our  ends 
if  we  alienate  the  sympathy  of  our  pupils  by  boring  them 
with  the  moral  which  they  can  quite  well  draw  for  them- 
selves. The  moral  may  be  insinuated  with  much  less 
chance  of  opposition  at  the  beginning  or  in  the  course 
of  the  story.1  The  end  is  the  fatal  place,  probably  be- 
cause the  interest  has  naturally  run  down  just  at  this 
point.  The  formality  and  the  inevitableness  of  the 
moral  are  also  to  be  taken  into  account.  It  has  all 
the  unpleasantness  of  the  bill  that  is  presented  after 
the  feast  is  over.2 

The  story,  as  compared  with  the  moral,  represents 
example  as  compared  with  precept.  There  is  room  for 
both  in  teaching.  Each  has  its  special  function.  Not 
only  does  the  story  have  behind  it  all  the  influence  that 
belongs  to  imitation,  but  it  has  all  the  special  force 
that  comes  from  acting  on  one's  own  initiative.  If  we 
hear  a  story  and  ourselves  make  the  necessary  applica- 
tion to  our  own  case,  we  feel  that  it  is  we  who  are  teach- 
ing ourselves  and  not  others  who  are  teaching  us. 
This  is  why  people  in  high  positions  in  ancient  times 

1  In  Section  50  of  the  Vorschule  der  Aesthetik,  Jean  Paul  Richter 
says :  "   ...  so  wie  die  Moral  aus  der  Fabel  leichter  zu  ziehen,  als 
die  Fabel  aus  der  Moral.     Ich  wurde  daher  (auch  aus  andern  Grtlnden) 
die  Moral  vor  die  Fabel  stellen."     We  have  here,  in  fact,  a  special 
case  of  the  problem  of  the  Zielangabe. 

2  With  regard  to  the  formulation  of  the  moral,  see  Chapter  VI, 
p.  151. 


THE  STORY  AS  ILLUSTRATION  269 

appear  to  have  accepted  in  the  form  of  fables  lessons 
that  would  have  cost  the  head  of  anyone  who  dared 
to  present  them  in  the  form  of  precepts.  A  divine 
writing  in  favour  of  the  use  of  religious  anecdotes  tells 
us:  — 

"Even  though  silenced,  people  are  not  readily  convinced  and 
influenced  by  mere  argument  .  .  .  narrating  an  instance  of  the 
effects  of  evil  conduct  often  tells  more  loudly  than  a  lecture  against 
it,  because  men  more  readily  imagine  fallacy  in  our  logic  than 
falsehood  in  our  narrative  of  incidents,  especially  when  associated 
with  the  life  of  some  noted  individual."  x 

It  is  not  a  matter  of  logic  at  all,  but  of  psychology. 
We  react  differently  to  a  lesson  according  as  it  is  pre- 
sented to  us  by  another  or  presented  by  ourselves  to 
ourselves.  Further,  the  association  "with  the  life  of 
some  noted  individual"  is  a  dramatic  touch,  and  has 
little  enough  to  do  with  truth  or  morality.  The  story 
of  Nathan  Rothschild  given  above  would  lose  a  great 
deal  of  its  dramatic  point  if  it  were  told  merely  about 
"a  certain  financier."  But  on  the  other  hand,  the  use 
of  such  a  well-known  name  leads  to  the  very  question- 
ings that  Mr.  Macleod  would  have  us  believe  are 
avoided  by  attaching  our  story  to  a  definite  person. 
Investigators  find  that  the  Waterloo  story  is  as  false  hi 
fact  as  it  is  in  teaching.2 

1  Norman  Islay  Macleod :  Moral  and  Religious  Anecdotes,  Preface. 

2  Rothschild  was  in  London  when  Waterloo  was  fought.     By  means 
of  a  specially  effective  system  of  communication  he  received  the  news 
of  the  Sunday's  battle  by  Monday  night,  and  intimated  it  to  Lord 
Liverpool  on  Tuesday  morning.     But  as  his  Lordship  had  only  a 
"  thin,  lazy  "  faith,  he  did  not  credit  the  news.    On  Tuesday  afternoon 
a  second  of  Rothschild's  couriers  brought  by  another  route  confirma- 
tion of  the  news ;  but  Lord  Liverpool  was  still  unconvinced ;  and  as  a 
matter  of  fact  it  was  thirty  hours  after  this  second  courier  had  been 
interviewed  that  the  official  despatches  came  from  Wellington  him- 


270    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

The  question  is  sometimes  asked  :  What  are  the 
qualities  of  a  good  illustrative  story?  It  is  easily 
answered  in  a  negative  way  at  least :  the  good  illustra- 
tive story  must  possess  all  the  qualities  that  make  an 
ordinary  story  good.  With  advanced  classes,  illustra- 
tive stories  should  be  short  and  pointed  —  in  the  sense 
of  having  one  point,  not  many.  With  young  children 
it  is  wise  to  keep  in  view  the  general  experience  effect, 
even  when  the  story  is  being  used  for  moral  ends.  A 
certain  lavishness  is  desirable  in  story-telling  for  the 
young.  We  are  told  that  the  Fables  of  La  Fontaine, 
charming  as  they  are,  still  fall  far  short  of  rousing  the 
enthusiasm  that  rewards  the  telling  of  tales  by  writers 
infinitely  inferior  to  the  French  fabulist.  The  explana- 
tion offered  is  that  the  fables  are  too  concise.  No 
sooner  has  the  child  warmed  up  to  his  work  than  the 
tale  has  ended.  It  is  not  so  much  that  the  child  objects 
to  the  moral  —  it  is  well  known  that  young  children 
are  themselves  somewhat  severe  moralists,  and  if  left 
to  themselves  would  supply  much  more  drastic  penalties 
than  the  ordinary  fabulist  would  sanction  —  as  that  he 
has  hardly  had  time  to  lose  himself  in  fable-land  before 
he  is  rudely  reawakened  to  the  realities  of  life.  It  is  in 
this  way  that  one  can  account  for  the  tolerance  of,  and 
even  the  preference  for,  somewhat  long  and,  to  older 
people,  rather  dreary  stories.  The  child  enjoys  the 
sustained  atmosphere  of  other-worldliness,  and  at  the 
same  tune  gains  practice  in  dealing  deliberately  with 

self.  Rothschild  certainly  operated  on  the  stock  exchange,  but  he  was 
far  from  keeping  his  news  a  secret.  Had  Liverpool  believed  him  at 
once,  his  Lordship  might  have  had  a  share  of  the  two  millions.  See 
an  interesting  article  by  Lucien  Wolf  in  the  Saturday  Westminster 
Gazette  (London)  for  June  26,  1909. 


THE  STORY   AS  ILLUSTRATION  271 

the  elements  that  make  up  the  world  of  thought, 
whether  regarded  from  the  point  of  view  of  imagination 
or  of  reality. 

For  this  last  reason  it  is  particularly  necessary  that  in 
the  stage  that  succeeds  the  fairy  tale  the  illustrative 
story  should  be  in  its  details  consistent  with  the  facts 
of  life.  The  pupil  should  be  able  to  learn  from  the 
story  in  an  indirect  way  a  great  many  facts,  and  must 
not  be  misled  by  having  impossibilities  introduced  into 
a  story  that  is  not  honestly  labelled  "  marvellous." 

With  older  people,  who  can  make  the  necessary 
allowances,  liberties  may  be  taken  with  literal  truth, 
though  artistic  truth  must  be  preserved.  Wordsworth 
is  not  very  happy  in  his  proclamation  at  the  beginning 
of  The  Westmoreland  Girl:  — 

"  Seek  who  will  delight  in  fable, 
I  shall  tell  you  truth." 

Everything  depends  on  the  kind  of  truth  one  has  in 
view.  Some  clergymen  will  not  use  any  story  the  literal 
truth  of  which  they  cannot  vouch  for.  While  this  re- 
striction seriously  limits  their  resources,  it  has  the  great 
compensating  advantage  that  it  prevents  them  from 
making  the  caricatures  of  real  life  that  pass  muster 
with  some  of  their  colleagues.  But  from  the  point  of 
view  of  teaching  there  is  nothing  against  invented  sto- 
ries, except  that  they  are  usually  very  badly  invented. 
Writers  on  the  theory  of  fiction  are  fond  of  telling  us 
that  really  high-class  fiction  is  truer  to  life  than  the 
things  that  happen  every  day.  But  while  The  Strange 
Case  of  Dr.  Jekyll  and  Mr.  Hyde  may  be  in  one  sense  more 
true  to  life  than  many  of  the  incidents  recorded  in  our 
morning  paper,  it  is  not  so  well  suited  for  certain  illus- 


272    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

trative  purposes  as  a  more  matter-of-fact  narrative. 
For  advanced  pupils  Stevenson's  story  forms  an  ad- 
mirable illustration,  since  they  can  make  abstraction  of 
the  supernatural  elements,  but  in  the  case  of  young 
pupils  the  story  is  not  suitable.  The  need  for  material 
accuracy  in  dealing  with  young  children  arises  naturally 
from  the  fact  that  the  story  in  their  case  has  to  serve 
the  double  function  of  illustrating  some  point  of  dis- 
course and  at  the  same  time  providing  material  and 
giving  opportunity  for  the  acquiring  of  new  experience 
of  things  in  general. 

Children  are  notoriously  fond  of  fairy  tales,  and  yet 
they  are  also  very  exacting  in  their  demand  for  truth  in 
the  stories  told  them.  There  is  no  real  contradiction 
involved.  Children  naturally  like  to  hear  of  wonderful 
things,  and  would  at  the  same  time  like  to  believe  that 
these  wonderful  things  really  happened.  Long  before 
school  age  the  child  keeps  its  fairy-tale  world  and  its 
real  world  quite  apart;  and  it  is  to  real-world  stories 
that  the  touchstone  of  truth  is  so  rigorously  applied. 
Fortunately,  at  early  stages  it  is  not  difficult  to  get  a 
sufficient  number  of  incidents  from  the  experience  of  the 
teacher  and  his  immediate  circle  supplemented  by 
what  is  available  in  the  way  of  printed  biography  to 
meet  the  needs  of  the  case;  and  at  later  stages  the  pupils 
acquire  the  power  of  detachment  that  enables  them  to 
see  the  truth  in  an  incident  that  they  are  not  sure  ever 
did  occur,  but  that  might  well  have  occurred.  It  is 
better  for  the  teacher  not  to  emphasise  the  fact  that  any 
particular  story  is  true,  as  the  main  effect  of  such  insist- 
ence is  to  make  the  children  recognise  that  all  the  other 
stories  are  not  true. 

It  is  difficult  to  say  exactly  what  degree  of  real 


THE  STORY  AS  ILLUSTRATION  273 

connection  should  be  insisted  on  between  the  story  and 
the  lesson  in  which  it  occurs;  for  the  degree  of  inge- 
nuity among  teachers  differs  so  much.  One  man  may 
introduce  almost  any  story  to  a  class  without  danger  of 
appearing  to  have  dragged  it  in.  Others  are  so  clumsy 
that  even  an  intrinsically  suitable  illustrative  story  has 
all  the  air  of  wondering  how  it  came  to  find  itself  there 
at  all.  I  have  on  my  bookshelves  several  volumes  of 
various  sizes  bearing  some  such  title  as  Moral  and  Reli- 
gious Anecdotes.  Some  of  them  are  published  plain. 
They  contain  stories  and  nothing  else.  They  are 
religious  Joe  Millers,  and  that  is  all.  Others  take 
a  higher  flight  and  classify  their  contents  so  that,  if  you 
wish  to  illustrate  Spiritual  Pride,  or  Worldly  Wisdom, 
or  Backbiting,  or  Fault-finding,  all  you  have  to  do  is  to 
turn  up  the  alphabetical  index  under  the  proper  letter, 
and  then  select  your  story  from  those  supplied.  This 
wooden  method  appeals  to  certain  minds,  but  it  gener- 
ally results  in  pedantic  dulness.  The  illustrations  are 
technically  right.  They  do  illustrate  the  heads  under 
which  they  are  placed.  The  stories  in  themselves  are 
usually  at  least  moderately  interesting;  but  somehow 
they  seem  to  lose  their  sparkle  when  they  are  passed 
through  the  alphabetical  sieve.  A  story  that  has  entered 
the  mind  of  the  teacher  without  prejudice  and  is  there 
worked  up  into  an  illustration  is  worth  many  gems 
culled  from  an  alphabetical  index.  An  experienced 
trainer  of  infant-school  teachers  under  the  London 
County  Council  urges  young  teachers  never  to  use  a 
story  till  they  have  "lived  with  it  for  three  months." 

The  teacher's  wisest  course  is  to  get  his  mind  filled 
with  the  subject  he  is  to  teach,  and  then  browse  about 
among  all  manner  of  books,  and  mix  with  all  manner 


274     EXPOSITION   AND  ILLUSTRATION   IN   TEACHING 

of  men.  Illustrative  incidents  will  occur  in  the  most 
unexpected  places.  It  must  not  be  forgotten  that  the 
mind  imposes  itself  upon  all  that  it  deals  with.  If  the 
mind  is  full  of  well-organised  masses  of  ideas  in  connec- 
tion with  a  given  subject,  it  cannot  help  fitting  all  the 
ideas  that  it  accepts  at  all  into  the  masses  that  domi- 
nate it  at  the  time. 


CHAPTER  XI 

ELABOKATION 

WE  have  seen  already  that  there  is  an  important  dis- 
tinction between  having  an  idea  and  realising  an  idea.1 
This  realisation  may  be  regarded  from  the  point  of  view 
of  intensity  or  from  that  of  complication.  To  realise 
the  idea  of  red  we  have  to  concentrate  the  consciousness 
in  such  a  way  as  to  reproduce  as  nearly  as  possible  the 
state  of  consciousness  that  accompanies  the  actual  sen- 
sation of  red.  But,  on  the  other  hand,  we  may  realise 
the  idea  of  church  by  allowing  to  come  into  the  con- 
sciousness all  the  elements  that  go  to  form  this  idea. 
When  Hobbes  calls  words  "the  counters  of  wise  men," 
he  means  that  we  can  use  words  as  a  sort  of  shorthand 
representation  of  concepts,  and  implies  that  we  are 
entitled  to  use  this  shorthand  only  on  condition  that 
we  are  able  to  transcribe  it  into  longhand  whenever 
we  are  called  upon  to  do  so.  In  ordinary  speech  we 
use  words  representing  such  complex  ideas  as  church, 
money,  bimetallism,  without  at  the  moment  of  using 
the  words  bringing  into  consciousness  more  than  an  in- 
finitesimal part  of  what  the  words  really  imply.  It  is 
assumed,  however,  that  if  called  upon  we  could  set  forth 
in  detail  all  the  elements  that  make  up  the  complex  idea 
we  are  dealing  with. 

It  is  true  that  very  often  when  we  proceed  to  elabo- 

1  See  p.  72 
275 


276     EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

rate  the  full  meaning  of  a  particular  idea  we  find  that  it 
does  not  by  any  means  contain  all  that  we  expected. 
We  go  through  the  world  largely  on  the  credit  of  a  ful- 
ness of  knowledge  that  is  not  there.  One  of  the  main 
purposes  of  the  Socratic  dialectic  was  to  expose  this 
ideational  bankruptcy.  Idea  after  idea  was  examined. 
The  interlocutor  was  invited  to  elaborate  it  as  far  as 
he  could  ;  and  the  result  was  nearly  always  that  great 
gaps  were  exposed.  When  a  pupil  sits  down  to  write  an 
essay,  he  is  really  entering  upon  an  exercise  in  elabora- 
tion. In  fact,  hi  the  schools  there  is  a  recognised  exer- 
cise under  the  name.  The  pupil  is  given  a  more  or  less 
pregnant  sentence  and  is  called  upon  to  bring  out  all  its 
implications.  When  Dr.  Arnold  invited  his  pupils  to 
write  on  The  Difference  between  Advantages  and  Merits, 
he  really  called  upon  them  to  allow  their  ideas  on  those 
subjects  to  develop  themselves,  and  then  to  compare 
and  contrast  the  results.  For  this  development  time 
must  be  allowed,  so  thinking  at  this  level  must  be  slow. 
There  is  naturally  a  very  great  gain  in  being  able  to  do 
our  thinking  on  the  Hobbes  credit  system.  If  we  regard 
thinking  as  the  adapting  of  means  to  ends  on  the  idea- 
tional plane,  it  follows  that,  if  we  can  get  at  our  ends 
without  developing  the  content  of  each  idea  as  it  oc- 
curs, we  effect  a  great  saving.  So  long  as  we  are  work- 
ing below  the  Inference  Point  there  is  obviously  no  need 
to  get  small  change  for  our  ideas.  In  matters  that 
fall  below  our  Inference  Point  the  ideas  are  so  welded 
together  in  causal  relations  that  we  cannot  use  them 
amiss  without  rousing  certain  oppositions  that  at  once 
come  into  consciousness,  and  raise  the  whole  subject 
up  to  the  Inference  Point,  and  therefore  secure  the  neces- 
sary investigation.  Obviously,  if  we  had  to  allow  each 


ELABORATION  277 

idea  to  elaborate  itself  every  time  we  used  it,  thinking 
would  become  impossible.  Even  at  the  Inference  Point 
we  do  not  require  to  make  a  complete  elaboration  of 
the  relevant  ideas  :  all  that  is  necessary  is  that  we  should 
arrange  them  so  that  their  potentialities  shall  be  awak- 
ened, and  raised  to  the  intensity  necessary  to  keep  them 
in  the  subconscious  state.  When  this  has  been  accom- 
plished, all  our  mental  content  that  is  relevant  to  the 
subject  under  discussion  is  in  an  excited  state,  so  that 
any  attempt  to  make  a  combination  inconsistent  with 
existing  combinations  will  be  at  once  checked  by  the 
rising  into  consciousness  of  the  relevant  existing  combi- 
nation and  the  consequent  opposition  to  the  proposed 
combination. 

It  is  not  till  we  have  reached  the  Gaping  Point  that 
it  becomes  necessary  to  allow  every  relevant  idea  to 
elaborate  itself  to  its  fullest  extent,  so  as  to  bring  into 
the  arena  all  the  elements  that  can  by  any  possibility 
have  anything  to  do  with  the  problem.  In  this  way 
we  give  the  mind  a  chance  of  making  the  combination 
that  will  reduce  the  unorganised  mass  to  order. 

A  special  kind  of  elaboration  is  that  which  takes  the 
form  of  turning  every  sort  of  idea  that  will  admit  of  it 
into  some  species  of  picture.  Many  people  are  unable 
to  carry  on  their  thinking  at  all  without  the  aid  of  some 
sort  of  pictorial  representation.  The  mental  pro- 
cesses of  such  people  may  be  compared  to  the  little 
retail  businesses  conducted  by  petty  traders,  all  of  whose 
financial  transactions  are  carried  on  by  means  of  coins 
of  small  denominations.  This  small-change  type  of 
thinking  is  regarded  with  great  contempt  by  some  of 
the  professional  philosophers.  Dr.  Hutchison  Stirling, 
for  example,  is  very  bitter  on  the  subject. 


278    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

"Now  it  is  this  association  of  ideas  that  constitutes  thought  to 
most  of  us  —  a  blind,  instinctive  secution  of  a  miscellaneous  multi- 
tude of  unverified  individuals.  These  individuals  are  Vorstellungen, 
figurate  conceptions  —  Ideas  —  crass,  emblematic  bodies  of  thoughts 
rather  than  thoughts  themselves.  Then  the  process  itself,  as  a 
whole,  is  also  nameable  Vorstellung  in  general.  An  example 
perhaps  will  illustrate  this.  'God  might  have  thrown  into  space  a 
single  germ-cell  from  which  all  that  we  see  now  might  have  developed 
itself.'  .  .  .  What  is  involved  in  this  writing  is  not  thought  but 
Vorstellung.  In  the  quotation  indeed  there  are  mainly  three  Vor- 
stellungen —  God,  Space,  and  a  Germ-cell.  Now  with  these  ele- 
ments the  writer  of  this  particular  sentence  conceives  himself  to 
think  a  beginning.  To  take  all  back  to  God,  Space,  and  a  single 
Germ-cell,  that  is  enough  for  him  and  his  necessities  of  thought ; 
that  to  him  is  to  look  at  the  thought  beginning  sufficiently  closely. 
But  all  these  three  elements  are  already  complete  and  self-dependent, 
—  God,  one  Vorstellung,  finished,  ready-made,  complete  by  itself, 
takes  up  a  Germ-cell,  another  Vorstellung,  finished,  ready-made, 
complete  by  itself,  and  drops  it  into  Space,  a  third  Vorstellung 
finished,  ready-made,  complete  by  itself.  This  done  —  without 
transition,  without  explanation,  the  rest  (by  the  way  another 
Vorstellung)  follows:  and  thus  we  have  three  elements  with  no 
beginning  —  at  the  same  time  that  we  have  four  with  no  transi- 
tion —  but  the  fiat  of  the  writer.  This,  then,  is  not  thought,  but  an 
idle  misspending  of  the  time  with  empty  pictures."  l 

We  need  not  take  this  diatribe  too  seriously.  As  to 
"thinking  a  beginning,"  Dr.  Stirling  is  no  doubt  right. 
This  demands  the  highest  degree  of  abstraction.  But 
there  is  a  place  for  figurative  thinking  as  well.  A  little 
further  on  in  the  Preface  Dr.  Stirling  himself,  re- 
luctantly, it  is  true,  and  within  brackets,  but  still  quite 
clearly,  admits  that  there  is  another  side  :  "(We  shall 
see  a  side  again  where  our  abstractions  are  to  be  re- 
dipped  hi  the  concrete,  in  order  to  be  restored  to  truth ; 

1  Preface  to  the  original  edition  of  The  Secret  of  Hegel,  p.  xl  (ed. 
1898). 


ELABORATION  279 

but  the  contradiction  is  only  apparent)."  Even  the 
playing  with  pictures  is  far  from  being  an  idle  mis- 
spending of  time.  At  certain  stages  and  in  certain  sub- 
jects pictorial  thinking  has  a  useful  function.  Why 
need  the  pictures  be  empty  ?  Here  is  what  a  French 
philosopher  has  to  say  on  the  other  side :  — 

" '  Picturing  is  not  reasoning '  [Image  n'est  pas  raison]  people  some- 
times say.  This  is  a  great  mistake.  There  is  nothing  more  lucid, 
more  enlightening  [explicatif]  than  certain  images.  One  is  sure  of 
having  an  idea  that  is  truly  intelligible  when  one  is  able  actually 
to  conceive  it,  that  is  to  say,  to  bring  it  back  to  an  intuition  or  a 
representation.  To  translate  an  abstract  idea  into  images  is  to 
prove  that  it  can  be  resolved  into  positive  conceptions.  This  is  to 
make  it  seen,  touched,  understood."  l 

Herbert  Spencer  clearly  believes  that  all  our  thinking 
is  figurative,  as  may  be  inferred  from  the  following 

passage :  — 

"As  we  do  not  think  in  generals  but  in  particulars  —  as,  when- 
ever any  class  of  things  is  referred  to,  we  represent  it  to  ourselves 
by  calling  to  mind  individual  examples  of  it.  .  .  ."  2 

It  is  certainly  too  strong  to  say  that  we  never  think 
in  generals,  but  the  possibility  of  thinking  in  generals 
in  no  way  militates  against  the  contention  of  Souriau 
and  Spencer  that  we  can  and  do  think  by  means  of 
images.  Even  in  the  case  of  those  who  deny  that  they 
have  any  power  of  forming  mental  imagery,  it  is  prob- 
able that  imagery  of  some  sort  is  present.  Speaking 
of  the  loss  among  scientific  men  of  the  power  of  visual 
representation,  Mr.  Francis  Galton  tells  us:  — 

"The  highest  minds  are  probably  those  in  which  it  is  not  lost, 
but  subordinated,  and  is  ready  for  use  on  suitable  occasions.  I  am, 

1  Paul  Souriau :  La  Suggestion  dans  I' Art,  p.  233. 

2  Essays,  stereotyped  edition,  1868,  Vol.  II,  p.  15. 


280    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

however,  bound  to  say,  that  the  missing  faculty  seems  to  be  re- 
placed so  serviceably  by  other  modes  of  conception,  chiefly,  I 
believe,  connected  with  the  incipient  motor  sense,  not  of  the  eyeballs 
only,  but  of  the  muscles  generally,  that  men  who  declare  themselves 
entirely  deficient  in  the  power  of  seeing  mental  pictures  can  never- 
theless give  life-like  descriptions  of  what  they  have  seen,  and  can 
otherwise  express  themselves  as  if  they  were  gifted  with  a  vivid 
visual  imagination.  They  can  also  become  painters  of  the  rank  of 
Royal  Academicians."  l 

There  may  not,  therefore,  be  the  fundamental  differ- 
ence that  Dr.  Hutchison  Stirling  would  have  us  believe 
between  his  thinking  and  that  carried  on  by  the  ordi- 
nary person.  For  us  the  important  point  at  present  is 
that  some  land  of  imagery  is  of  the  very  essence  of  Illus- 
tration. Many  people,  after  hearing  a  purely  abstract 
statement  of  some  argument,  are  quite  at  a  loss  till  they 
have  translated  it  into  a  series  of  pictures.  Some  of 
my  friends  in  the  philosophical  faculty  begin  each  new 
session  with  the  resolve  that  they  will  approach  meta- 
physics in  a  more  concrete  way.  Their  experience  is 
that  the  students  can  understand  each  of  the  paragraphs 
by  itself,  but  that  because  of  the  total  lack  of  imagery 
they  cannot  grasp  the  subject  of  a  lecture  as  a  whole. 
The  practical  teacher  is  much  more  safe  with  an  excess 
on  the  side  of  the  concrete.  But  a  caution  is  not  per- 
haps out  of  place  at  this  point.  In  the  schoolroom 
so  many  caveats  are  entered  against  the  abstract  that 
among  our  younger  teachers  who  have  had  some  theoreti- 
cal training  there  is  a  tendency  to  regard  the  abstract 
as  something  in  itself  to  be  avoided.  Certainly  we 
must  begin  with  the  concrete.  There  is  very  general 
agreement  with  the  formula :  From  the  concrete  to  the 

1  Inquiries  into  Human  Faculty  and  its  Development,  Everyman's 
Library,  p.  61. 


ELABORATION  281 

abstract.  But  after  all,  this  places  the  abstract  in  the 
honourable  position  of  being  the  goal  of  our  teaching. 
The  trammels  of  the  concrete  must  be  thrown  off,  so 
that  our  pupils  may  enter  the  freer  medium  of  the 
abstract.  Further,  there  must  be  no  divorce  be- 
tween the  two.  The  abstract  must  be  always  capable 
of  being  expressed  in  terms  of  the  concrete.  There 
are  occasions,  of  course,  on  which  the  introduction 
of  the  concrete  only  clogs  the  wheels  of  thought, 
but  there  are  others  in  which  the  abstract  thinker 
is  saved  from  error  by  continual  reference  to  the 
concrete. 

The  element  of  time  has,  of  course,  to  be  taken  into 
account.  We  sometimes  hear  such  phrases  as  "with 
the  swiftness  of  thought,"  and  some  people  appear  to 
believe  that  thought  takes  no  time  at  all.  All  thinking 
takes  an  appreciable  time,  but  the  kind  that  best  de- 
serves the  rank  of  being  a  standard  of  speed  is  the  kind 
that  does  not  hamper  itself  with  images.  To  carry 
on  a  train  of  thought  by  means  of  imagery  demands 
quite  a  considerable  time.  Still,  the  important  question 
is  whether  this  time  is  wasted  or  well  spent. 

The  struggle  between  the  abstract  and  the  concrete 
becomes  acute  in  discussions  concerning  the  teaching  of 
arithmetic.  Some  teachers  regard  the  abacus  with 
suspicion,  and  look  askance  at  all  the  infant  school 
paraphernalia  of  beans  and  balls  and  bricks.  They 
are  afraid  that  children  will  acquire  the  concrete  habit, 
and  will  go  through  life  on  the  bean  level  of  calculation. 
In  the  case  of  "fingering"  there  is  certainly  a  danger 
from  the  fatal  convenience  of  this  means  of  counting, 
but  as  a  matter  of  fact  the  child  soon  tires  of  the  limita- 
tions imposed  by  the  beans  and  bricks,  and  seeks  the 


282    EXPOSITION  AND   ILLUSTRATION   IN  TEACHING 

freedom  of  abstraction  as  soon  as  he  finds  that  he  can 
calculate  without  them.  In  arithmetic  we  need  never 
want  to  get  beyond  the  concrete  in  applying  its  prin- 
ciples. Teachers  are  too  apt  to  regard  arithmetic  as 
something  important  by  itself;  to  take  the  view  of  the 
mathematical  savant  who  rejoiced  that  a  certain  theo- 
rem he  had  promulgated  could  not  be  used  for  anything 
practical.  The  truth  of  the  matter  is  that  arithmetic 
is  only  a  particularly  abstract  way  of  regarding  common 
things.  The  danger  of  excessive  abstractness  is  no- 
where better  illustrated  than  in  those  sections  of  our 
arithmetic  text-books  that  elaborate  certain  rules  for 
dealing  with  particular  classes  of  concrete  matters. 
Stocks  and  shares  are  marked  off  from  mere  percentages, 
and  weird  headings  such  as  Alligation  are  used  to  keep 
certain  matters  in  their  special  corner.  The  same  sort 
of  thing  began  in  algebra  text-books,  but  has  fortunately 
had  rather  a  set-back  of  late.  The  requirements  of 
examinations  made  it  worth  the  specialist's  while  to 
classify  the  sort  of  problems  set,  and  we  were  beginning 
to  have  " rules"  for  clock  problems,  hare  and  hound 
problems,  bath  problems,  age  problems.  Fortunately, 
teachers  are  realising  that  this  is  carrying  abstraction 
too  far.  The  rule  must  not  be  regarded  as  a  means  of 
saving  all  thought  with  regard  to  the  matter  to  which 
it  is  to  be  applied.  The  place  of  the  abstract  is  between 
the  stating  of  the  equation  and  its  solution.  It  must 
begin  with  the  concrete,  and  at  the  end  it  must  square 
its  results  with  the  concrete.  In  the  middle  of  the 
working  of  the  problem  we  cannot  say  what  relation 

35  it 

-~  has  to  the  hands  of  a  clock,  but  so  soon  as  the 

lo 

operator  rises  again  to  the  "answer"  we  are  once  more 


ELABORATION  283 

in  the  region  of  the  concrete,  and  our  results  must 
stand  the  test  of  comparison  with  the  concrete. 

It  must  not  be  forgotten  that  thinkers  who  are  able 
to  soar  into  the  empyrean  of  the  Hutchison  Stirling 
abstractions  have  gained  their  power  of  flight  by 
mastering  the  relevant  concrete,  and  that  the  results  of 
their  high  thinking  must  at  least  not  contradict  the 
concrete  itself,  though  it  need  not  be  consistent  with  the 
quasi-abstract  views  that  the  less  free  thinkers  obtain 
by  the  help  of  Vorstellungen.  The  teacher  very  often 
occupies  the  position  of  the  abstract  thinker  who  has 
reached  a  certain  conclusion  that  he  can  help  his  pupil 
to  reach  only  by  the  aid  of  certain  figurate  conceptions. 
The  development  of  Vorstellungen  in  the  mind  natu- 
rally takes  time,  but  the  time  is  not  necessarily  wasted. 
From  the  figures  the  mind  of  the  pupil  may  rise  to  a 
complete  understanding  of  the  underlying  principle,  and 
so  secure  his  freedom.  But  while  we  are  at  the  figurate 
stage  it  is  necessary  to  go  at  an  appropriate  pace. 
We  must  hasten  slowly,  in  order  that  we  may  get  the 
full  advantage  of  the  stage  at  which  our  pupil  stands. 
We  must  allow  ideas  to  elaborate  themselves  so  that  the 
full  content  may  be  examined.  Very  often  illustration 
consists  of  nothing  else  than  giving  complex  ideas  a 
chance  to  develop  in  consciousness  in  a  natural  way. 
Some  pupils  may  be  unable  to  understand  an  explana- 
tion that  the  majority  of  their  class-mates  have  found 
to  be  perfectly  clear.  Before  seeking  out  some  new 
form  of  statement  it  is  often  well  to  see  what  can  be 
done  by  getting  the  pupils  to  allow  the  ideas  represented 
by  the  words  used  in  the  explanation  to  develop  them- 
selves in  their  consciousness.  When  each  of  the  ideas 
concerned  is  allowed  to  develop  its  implications,  it 


284    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

results  that  certain  relations  become  manifest  that 
would  otherwise  have  remained  hidden. 

Minds  differ  greatly  in  their  power  to  give  ideas  a 
chance  to  develop  their  implications.  Too  often  what 
happens  when  an  attempt  is  made  to  allow  an  idea  to 
unfold  its  meaning  is  that  at  the  second  or  third  remove 
from  the  surface  meaning  the  consciousness  is  switched 
off  into  some  other  series  of  ideas  connected  by  a  more 
or  less  loose  bond  of  association  with  the  initial  idea. 
What  Professor  Stout  calls  "psychic  fringes"1  have  to 
be  taken  account  of  here.  Each  idea  has  its  own  fringe, 
and  when  several  ideas  are  being  developed  at  once  there 
is  a  certain  amount  of  interference  caused  by  these 
fringes.  Sometimes  the  struggle  of  the  various  fringes 
is  so  keen  that  further  development  is  impossible,  and 
some  entirely  new  idea  through  a  side  association  slips 
its  way  into  the  consciousness  and  drives  out  the  ideas 
that  have  been  trying  to  develop  themselves.  It  is 
necessary,  therefore,  that  the  teacher  should  be  ready 
with  some  help  to  the  particular  ideas  he  wishes  to  be 
allowed  to  develop.  Sometimes,  indeed,  it  comes  about 
that  the  mere  enumeration  by  the  teacher  of  the  ele- 
ments of  a  compound  conception  may  be  helpful  to  a 
certain  class  of  mind.  Many  of  our  best  writers  illus- 
trate this  need  by  the  construction  of  their  paragraphs. 
The  first  sentence  enunciates  the  real  substance  of  the 
paragraph;  all  the  rest  is  an  elaboration  of  the  mean- 
ing contained  in  that  first  sentence.  When  Macaulay 
has  said  of  Horace  Walpole:  "The  conformation  of  his 
mind  was  such  that  whatever  was  little  seemed  to  him 
great,  and  whatever  was  great  seemed  to  him  little,"  he 
has  given  us  the  whole  substance  of  the  paragraph  that 

1  Analytical  Psychology,  Vol.  I,  p.  92  ff. 


ELABORATION  285 

the  sentence  introduces.  Yet  when  we  turn  to  the  elabo- 
ration of  the  idea  as  contained  in  the  rest  of  the  para- 
graph, we  realise  that  we  understand  it  in  a  much  fuller 
sense  than  we  did  before  we  had  read  the  whole  para- 
graph :  — 

"...  Serious  business  was  a  trifle  to  him,  and  trifles  were  his 
serious  business.  To  chat  with  blue-stockings,  to  write  little  copies 
of  complimentary  verses  on  little  occasions,  to  superintend  a  private 
press,  to  preserve  from  natural  decay  the  perishable  topics  of  Rane- 
lagh  and  White's,  to  record  divorces  and  bets,  Miss  Chudleigh's  ab- 
surdities and  George  Selwyn's  good  sayings,  to  decorate  a  grotesque 
house  with  pie-crust  battlements,  to  procure  rare  engravings  and 
antique  chimney-boards,  to  match  odd  gauntlets,  to  lay  out  a  maze 
of  walks  within  five  acres  of  ground,  these  were  the  grave  employ- 
ments of  his  long  life.  From  these  he  turned  to  politics  as  to  an 
amusement.  After  the  labours  of  the  print-shop  and  the  auction 
room,  he  unbent  his  mind  in  the  House  of  Commons.  And  having 
indulged  in  the  recreation  of  making  laws  and  voting  millions, 
he  returned  to  more  important  pursuits,  to  researches  after  Queen 
Mary's  comb,  Wolsey's  red  hat,  the  pipe  which  Van  Tromp  smoked 
during  his  last  sea-fight,  and  the  spur  which  King  William  struck 
into  the  flank  of  Sorrel." 

Obviously  the  specific  cases  in  which  Walpole  exempli- 
fies the  weakness  with  which  he  is  charged  in  the  first 
sentence  form  legitimate  illustrations  of  the  theme. 
In  such  a  case  the  expositor  is  assumed  to  have  know- 
ledge of  certain  facts  that  may  not  be  in  the  possession 
of  the  pupil.  Sometimes  elaboration  takes  the  form  of 
merely  setting  forth  in  a  vivid  way  certain  aspects  of  the 
original  statement.  This  presentation  does  not  imply 
any  special  knowledge  on  the  part  of  the  illustrator. 
Any  of  his  readers  may  do  the  same  for  themselves  from 
the  material  supplied,  if  only  they  have  imagination 
enough.  Sir  A.  Conan  Doyle  has  an  excellent  passage 1 

1  The  Great  Shadow,  p.  6. 


286    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

that  exemplifies  both  these  forms  of  elaboration.  The 
narrator  of  the  story  wishes  to  convey  an  idea  of  what 
the  Napoleonic  wars  really  meant  to  England.  He 
begins  by  a  reference  to  his  father:  — 

"When  he  died  we  had  been  fighting  with  scarce  a  break,  save 
only  during  two  short  years,  for  very  nearly  a  quarter  of  a  century. 
Think  of  it,  you  who  live  so  quietly  and  peacefully  now !  Babies 
who  were  born  in  the  war  grew  to  be  bearded  men  with  babies  of 
their  own,  and  still  the  war  continued.  Those  who  had  served  and 
fought  in  their  stalwart  prime  grew  stiff  and  bent,  and  yet  the  ships 
and  the  armies  were  struggling.  It  was  no  wonder  that  folk  came 
at  last  to  look  upon  it  as  the  natural  state,  and  thought  how  queer  it 
must  seem  to  be  at  peace." 

Down  to  this  point  the  author  is  simply  working  out 
in  a  vivid  way  conceptions  that  anyone  with  a  keen 
appreciation  of  the  situation  could  elaborate  for  him- 
self from  the  data  assumed.  This  is  a  form  of  elabora- 
tion that  is  of  special  value  in  the  schoolroom.  The 
rest  of  the  paragraph  proceeds  on  the  ordinary  line  of 
elaboration  that  adds  new  matter  while  illustrating  the 
main  point. 

"During  that  long  time  we  fought  the  Dutch,  we  fought  the 
Danes,  we  fought  the  Spanish,  we  fought  the  Turks,  we  fought  the 
Americans,  we  fought  the  Monte- Videans,  until  it  seemed  that  in 
this  universal  struggle  no  race  was  too  near  of  kin,  or  too  far  away,  to 
be  drawn  into  the  quarrel.  But  most  of  all  it  was  the  French  whom 
we  fought,  and  the  man  whom  of  all  others  we  loathed  and  feared 
and  admired  was  the  great  Captain  who  ruled  them." 

There  is  a  still  easier  form  of  elaboration  that  con- 
fines itself  to  simple  Enumeration  of  elements  that  are 
implicit  in  the  original  conception,  and  could  be  supplied 
by  the  most  ordinary  listener  or  reader.  No  special 
keenness  of  observation,  no  gift  of  imagination,  is  re- 
quired. We  have  seen  that  suggestion  acts  instantane- 


ELABORATION  287 

ously  in  recalling  all  there  is  to  recall  of  a  given  whole. 
The  poet  makes  his  suggestion,  appeals  to  his  reader, 
and  leaves  the  rest  to  him.  That  is,  the  ordinary  poet 
does  this.  For  there  is  an  extraordinary  class  of  poets 
who  seek  to  save  their  readers  time  and  trouble  by 
enumerating  in  detail  all  the  elements  that  are  implicit 
in  the  ideas  suggested  in  a  poem.  Walt  Whitman  is  a 
notorious  sinner  in  this  way.  He  is  preeminently  the 
poet  of  the  catalogue.  He  wishes,  for  example,  to 
emphasise  the  very  common  feeling  that  occasionally 
occurs  to  all  of  us  of  the  variety  of  experiences  that  are 
going  on  at  every  moment  of  every  day.  Accordingly, 
he  selects  the  probable  conditions  and  doings  of  all  the 
sailors  of  the  globe.  He  gives  a  long  catalogue,  that 
reads  like  a  quotation  from  a  gazetteer,  of  the  places 
where  sailors  are  likely  to  be  found,  and  another  of  the 
sort  of  things  they  are  likely  to  be  doing.  The  nature 
of  the  list  may  be  inferred  from  the  concluding  line:  — 

"Some  with  infectious  diseases." 

Lest  it  should  be  supposed  that  this  description  is  ex- 
aggerated, it  may  be  well  to  quote  one  of  the  poet's 
catalogues.  This  time  he  wishes  us  to  realise  the  great 
variety  of  things  that  may  be  made  out  of  wood,  and 
helps  our  jaded  imagination  with  the  following  inven- 
tory:— 

"The  axe  leaps! 

The  solid  forest  gives  fluid  utterances, 
They  tumble  forth,  they  rise  and  form, 
Hut,  tent,  landing,  survey, 
Flail,  plough,  pick,  crowbar,  spade, 
Shingle,  rail,  prop,  wainscot,  jamb,  lath,  panel,  gable, 
Citadel,  ceiling,  saloon,  academy,  organ,  exhibition-house,  library, 
Cornice,  trellis,  pilaster,  balcony,  window,  turret,  porch, 


288    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

Hoe,  rake,  pitchfork,  pencil,  waggon,  staff,  saw,  jack-plane,  mallet, 

wedge,  rounce, 

Chair,  tub,  hoop,  table,  wicket,  vane,  sash,  floor, 
Workbox,  chest,  string'd  instrument,  boat,  frame,  and  what-not."  l 

Contrast  this  crude  catalogue  with  the  following 
lines  in  which  Tennyson  apostrophises  the  vessel  that  is 
bringing  home  the  remains  of  his  friend :  — 

"  I  hear  the  noise  about  thy  keel ; 

I  hear  the  bell  struck  in  the  night : 
I  see  the  cabin-window  bright ; 
I  see  the  sailor  at  the  wheel. 

Thou  bring'st  the  sailor  to  his  wife, 

And  travelTd  men  from  foreign  lands ; 
And  letters  unto  trembling  hands ; 

And,  thy  dark  freight,  a  vanish 'd  life."  * 

Here  the  reader  gets  real  help  from  the  elaboration. 
After  reading  the  lines  he  has  a  better  picture  of  the 
whole  scene  than  he  had  before.  The  poet  has  selected 
the  most  effective  elements  in  the  night  scene.  The 
"bell  struck  in  the  night"  appeals  to  all,  as  is  shown 
by  the  effect  it  produces  when  used  on  the  stage,  while 
the  "cabin- window  bright"  is  one  of  the  most  striking 
sights  at  sea,  even  though  it  did  annoy  Kipling's  tramp 
captain. 

It  may  be  said  that  Whitman  should  not  be  compared 
with  Tennyson  but  with  Homer,  whose  catalogues  of 
ships  and  states  and  heroes  may  appear  to  give  some 
justification  to  the  modern  maker  of  poetical  catalogues. 
There  were,  however,  more  than  merely  rhetorical  rea- 
sons for  the  appearance  of  these  lists  in  Homer's  pages, 
though  it  must  be  admitted  that  they  also  served  rhe- 

1  Song  of  the  Broad-Axe  from  Leaves  of  Grass. 
1  In  Memoriam,  X. 


ELABORATION  289 

torical  ends  and  served  them  well.  It  is  interesting  to 
note  that  the  love  of  lists  is  characteristic  of  primitive 
writing,  and  that  this  same  love  is  also  apparent  among 
young  children.  Almost  every  successful  writer  for  little 
children  uses  the  artifice  of  elaborating  in  this  more  or 
less  arithmetical  way  all  ideas  that  lend  themselves  to 
it.  Passages  like  the  following  are  common  in  books 
for  the  young :  — 

"  Perhaps  you  do  not  believe  in  fairies !  Ah,  well,  I  am  sorry 
for  you.  I  believe  in  them,  in  every  one  of  them  —  gnomes  and 
sylphs,  and  fays  and  sprites,  and  elves  and  goblins  —  yes,  even  in 
ouches — though  some  don't.  There !  What  do  you  think  of  that  ?  "  * 

It  is  easy  to  see  why  young  people  should  find  a  sat- 
isfaction in  enumerating  the  content  of  a  given  idea. 
The  elements  have  not  yet  had  time  to  grow  stale  to  the 
young  mind.  There  is,  further,  the  sense  of  power 
implied  in  the  setting  forth  of  the  contents  of  the  mental 
treasure-house.  Nor  must  it  be  forgotten  —  and  the 
consideration  is  not  quite  irrelevant  to  our  present 
purpose  —  that  the  sense  of  rhythm  involved  in  the 
enumeration  of  the  elements  is  a  source  of  keen  satisfac- 
tion to  the  young,  and  is  not  without  its  attraction  for 
the  adult.  The  following  example  of  illustrative  enu- 
meration from  Dickens  exemplifies  at  once  the  charm  of 
rhythm  and  the  rhetorical  value  of  this  form  of  elabora- 
tion. The  purpose  is  to  throw  discredit  on  the  kind  of 
training  provided  for  elementary  teachers  in  England. 
The  method  is  to  elaborate  the  mental  content  of  what 
is  assumed  to  be  a  typical  elementary  schoolmaster. 
The  selected  type  is  named  M'Choakumchild,  and 
this  is  how  the  elaboration  is  carried  out:  — 

1  Rev.  J.  R.  Howatt :  The  Children's  Pulpit,  p.  270. 

u 


290    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

"He  and  some  one  hundred  and  forty  other  schoolmasters  had 
been  lately  turned  at  the  same  time,  in  the  same  factory,  on  the 
same  principles,  like  so  many  pianoforte  legs.  He  had  been  put 
through  an  immense  variety  of  paces,  and  had  answered  volumes  of 
head-breaking  questions.  Orthography,  etymology,  syntax,  and 
prosody,  biography,  astronomy,  geography,  and  general  cosmog- 
raphy, the  sciences  of  compound  proportion,  algebra,  land-sur- 
veying and  levelling,  vocal  music,  and  drawing  from  models 
were  all  at  the  ends  of  his  ten  chilled  fingers.  He  had  worked  his 
stony  way  into  Her  Majesty's  Most  Honourable  Privy  Council's 
Schedule  B,  and  had  taken  the  bloom  off  the  higher  branches  of 
mathematics  and  physical  science,  French,  German,  Latin,  and 
Greek.  He  knew  all  about  all  the  watersheds  of  all  the  world 
(whatever  they  are),  and  all  the  histories  of  all  the  peoples,  and  all 
the  names  of  all  the  rivers  and  mountains,  and  all  the  productions, 
manners,  and  customs  of  all  the  countries,  and  all  their  boundaries 
and  bearings  on  the  two-and-thirty  points  of  the  compass.  Ah ! 
rather  overdone,  M'Choakumchild.  If  he  had  only  learnt  a  little 
less,  how  infinitely  better  he  might  have  taught  much  more."  * 

As  rhetoric  this  is  somewhat  unfair,  but  very,  very  ef- 
fective. Dickens  was  not  an  expert  reporter  for  nothing, 
and  a  better  example  of  deliberately  inflated  English  it 
would  be  hard  to  find.  It  is  notable  that  logic  does  not 
appear  among  the  subjects,  so  the  assaulted  M'Choak- 
umchild is  supposed  to  have  been  too  busy  with  general 
cosmography  to  have  had  time  to  learn  of  an  interest- 
ing little  fallacy  called  the  thaumatrope.  At  any  rate, 
Dickens  goes  on  using  his  material  over  and  over  again, 
as  if  his  readers  had  never  heard  of  Mr.  Caudle's  five- 
pound  note.  At  the  simple,  yet  in  this  case  magical, 
word  grammar,  four  of  the  most  appalling  words  on  the 
list  collapse,  while  the  commonplace  word  geography 
shrivels  up  nearly  all  that  is  left  of  the  bubble.  Yet 
it  cannot  be  denied  that  grammar  and  geography 

1  Hard  Times,  Book  I,  Chap.  II. 


ELABORATION  291 

do  include  the  elements  he  enumerates,  and  so  those 
subjects  are  made  to  appear  by  the  mere  process  of 
elaboration,  and  the  skilful  repetition  of  the  little  word 
all,  as  something  peculiarly  pretentious  and  unneces- 
sary. Dickens  has  here  a  clearly  denned  point  of  view, 
and  it  cannot  be  denied  that  he  has  admirably  illus- 
trated it. 

This  illustrative  enumeration  is  not  to  be  confounded 
with  that  form  of  illustration  that  consists  in  presenting 
a  great  series  of  different  complex  conceptions,  each  of 
which  has  some  element  common  to  all  the  others.  It 
is  not  a  process  of  analysing  out  the  common  element  in 
a  number  of  cases  and  so  coming  to  an  understanding  of 
the  principle  to  be  illustrated.  When  we  heap  figure 
upon  figure  to  get  the  cumulative  effect  of  recognising 
the  same  element  in  many  different  environments,  we 
enrich  the  conception  by  demonstrating  how  widely 
it  may  be  applied.  When  Burns  gives  us  his  series  of 
figures  illustrating  the  transitory  nature  of  pleasures :  — 

"But  pleasures  are  like  poppies  spread, 
You  seize  the  flow'r,  its  bloom  is  shed; 
Or  like  the  snowfalls  in  the  river, 
A  moment  white  —  then  melts  for  ever ; 
Or  like  the  borealis  race, 
That  flit  ere  you  can  point  their  place ; 
Or  like  the  rainbow's  lovely  form 
Evanishing  amid  the  storm."  ' 

we  feel  that  the  work  of  realising  these  fine  figures  is 
thrown  upon  us,  and  that  the  result  is  an  intensified 
awareness  of  the  fleetingness  of  human  delights.  This 
is  produced  by  the  fusion  of  the  common  element  in  the 
different  cases.  The  concrete  setting  of  each  of  the 

1  Tarn  o'  Shanter,  59-66. 


292    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

figures  performs  the  same  function,  and  these  set- 
tings must  therefore  be  regarded  as  falling  under  one 
category.  Consequently  they  have  to  be  treated  as 
contrary  ideas  which  arrest  each  other  and  thus  leave 
the  common  elements  free  to  coalesce. 

In  enumeration,  on  the  other  hand,  the  predominant 
force  at  work  is  that  of  complication,  though  this  pro- 
cess must  be  regarded  from  two  points  of  view,  accord- 
ing as  we  deal  with  the  pupil's  share  in  the  work  or  the 
teacher's.  Considered  from  the  pupil's  standpoint, 
elaboration  consists  in  the  breaking  up  of  a  complex  into 
its  elements.  From  the  teacher's  standpoint  it  consists 
in  supplying  a  large  number  of  elements  that  are  im- 
plicit in  the  whole  that  is  already  a  part  of  the  pupil's 
mental  content,  though  this  whole  is  rather  empty. 
When  the  teacher  proceeds  deliberately  to  enrich  the 
content  of  a  whole  that  he  knows  to  exist  in  the  mind  of 
the  pupil,  it  may  be  thought  to  be  rather  a  matter  of 
information  than  of  illustration.  Yet  since  the  given 
whole  is  the  starting-point,  and  the  process  results 
in  making  clearer  the  meaning  of  that  whole,  it  may 
not  unfairly  be  treated  as  a  case  of  illustration. 

Take  the  case  of  trying  to  enrich  the  pupil's  concep- 
tion of  the  state  of  affairs  at  any  particular  time  in  the 
history  of  the  world.  First  of  all,  he  should  be  invited 
to  bring  out  all  the  ideas  he  has  on  the  given  period. 
Here  the  pupil  allows  divergent  association  to  work. 
The  given  date  suggests  all  manner  of  diverse  things  that 
come  into  the  mind  one  after  the  other.  It  is  now  the 
teacher's  business  to  arrange  the  ideas  thus  called  up, 
and  to  supply  other  ideas  that  not  merely  enrich  the 
content  of  the  complex  idea  of  the  period,  but  place  the 
old  elements  in  a  new  light.  Often  all  that  is  necessary 


ELABORATION  293 

to  understand  two  disparate  ideas  is  the  presentation  of 
a  third  which  inevitably  leads  to  a  correlation  of  the 
two  first.  We  have  here  a  suggestion  of  the  illus- 
trative power  of  the  attendant  circumstance.  Fre- 
quently by  presenting  a  matter  in  very  great  detail  the 
teacher  succeeds  in  illustrating  it  by  giving  so  many 
starting-points  for  divergent  association  that  one  or 
other  of  them  must  lead  to  such  a  collocation  of  ideas 
as  shall  throw  light  upon  the  pupil's  difficulties. 

Victor  Hugo  devotes  a  brilliant  chapter  l  to  the  elabo- 
ration of  the  social  and  political  conditions  of  Paris  hi 
the  year  1817.  Here  he  takes  it  for  granted  that  his 
readers  know  the  details  that  he  sets  about  arranging 
into  an  organised  whole.  He  enumerates  the  well- 
known  persons  who  flourished  at  that  period,  and  indi- 
cates what  each  was  doing.  He  suggests  the  prevailing 
fashions  of  speech,  thought,  and  dress.  He  adds  illumi- 
nating sidelights  in  the  way  of  vivid  contrasts  between 
promise  and  performance,  between  real  and  apparent, 
between  the  trifling  and  the  significant.  The  effect  of 
the  chapter  is  that  the  reader  feels  that  there  was  a 
living  Paris  in  that  year,  and  is  ready  to  deal  intelli- 
gently with  any  events  that  transpired  then.  Still,  un- 
less one  knows  a  good  deal  about  the  France  of  that 
time,  one  is  not  in  a  position  to  profit  by  the  brilliant 
grouping  of  Hugo.  His  is  a  work  of  elaboration  and 
enumeration  rather  than  of  knowledge-giving.  This 
has  to  be  kept  in  view  in  our  teaching  of  history.  There 
is  a  strange  fallacy  still  somewhat  prevalent  regarding 
the  text-books  on  this  subject.  It  appears  to  be  thought 
that  the  size  of  the  text-book  should  vary  in  direct  ratio 
to  the  size  of  the  pupil :  Big  boy,  big  book ;  little  boy, 

1  Les  Mistrables,  Part  I,  Book  III,  Chap.  I. 


294    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

little  book;  whereas  the  sizes  should  be  in  inverse  ratio. 
The  beginner  in  history  should  have  a  great  deal  of 
detail;  he  is  preparing  the  material  that  will  afterwards 
be  used  when  he  is  called  upon  to  elaborate,  group,  and 
classify.  Teachers  are  now  so  eager  to  get  at  the  essen- 
tials of  history  that  they  forget  that  the  pupils  must 
acquire  a  certain  number  of  the  facts  of  history.  There 
is  naturally  no  need  to  worry  pupils  with  the  old  excess 
of  dates  and  genealogical  tables,  but  a  great  deal  of  wide 
general  reading  in  history  ought  to  precede  the  laud- 
able attempts  to  teach  constitutional,  and  what  may 
be  described  as  scientific,  history. 

Illustration  by  elaboration  finds  an  important  field  hi 
connection  with  definition  in  its  wider  sense.  To  give 
an  idea  of  what  Gothic  architecture  really  is,  we  must 
do  more  than  tell  our  pupils  that  it  is  that  form  of  archi- 
tecture that  prevailed  between  1200  A.D.  and  1475  A.D., 
and  is  marked  by  pointed  arches,  steep  roofs,  relatively 
large  windows,  and  great  height  in  proportion  to  the 
other  dimensions.  We  must  elaborate  by  calling  atten- 
tion to  many  different  specimens  of  this  kind  of  archi- 
tecture, and  by  enumerating  the  different  qualities  of 
each  so  as  to  give  content  to  the  somewhat  empty 
definition. 

Few  words  are  more  difficult  to  define  than  bourgeois. 
The  following  attempt l  takes  the  form  of  elaboration, 
and  is  therefore  well  suited  to  illustrate  this  section :  — 

"To  call  a  person  or  an  institution  bourgeois  is  for  her  [Madame 
de  Coulevain]  the  very  worst  degree  of  condemnation.  '  Foreigners,' 
she  writes, '  often  ask  me  the  meaning  of  the  term  bourgeois.  I  find 

1  Winifred  Stephens,  French  Moralists  of  To-day,  1908.  Chapter  on 
Pierre  de  Coulevain,  p.  94. 


ELABORATION  295 

it  very  difficult  to  define.  .  .  .  Bourgeoisisme,  like  provincialism, 
is  a  mentalite.  ...  It  communicates  a  shell-like  impenetrability. 
Its  characteristics  are  to  be  found  in  people  who  have  received  a 
superior  culture,  in  whom  are  developed  taste  and  a  sense  of  beauty. 
It  betrays  itself  by  common  ideas,  extreme  intolerance,  blind  obsti- 
nacy, an  incapacity  above  all  things  to  understand  and  to  accord 
liberty.  This  mentalite  creates  a  particular  and  unmistakable 
atmosphere.  The  peasant,  the  workman,  the  artisan  are  not 
bourgeois.  I  might  name  a  king  who  is  more  so  than  many  people 
born  in  the  Rue  du  Sentier.  Napoleon  I  was  bourgeois.  Napoleon 
III  was  not.  Balzac,  Guy  de  Maupassant  were  not  bourgeois; 
Zola,  was.  Two  of  our  great  newspapers,  one  of  our  best  reviews  are. 
The  church  of  Saint  Augustin  is  bourgeois,  Saint  Roch  is  not.  The 
Come"die  Francaise,  the  Ope"ra  Comique,  the  Palais  Royal  are  bour- 
geois; the  Vaudeville,  the  Varie'te's,  the  Theatre  Antoine,  the 
caf£s  concerts  of  Montmartre  are  not.  Among  the  tea-houses  all 
are,  with  one  exception.  England,  Italy,  Spain  are  not  bourgeoise; 
Germany  is  and  her  emperor  is  not.'  Until  this  last  sentence 
(thanks  to  Madame  de  Coulevain's  kind  explanation),  we  had  im- 
agined ourselves  beginning  to  understand  the  meaning  of  this 
enigmatical  term ;  but  if  the  German  Emperor  be  not  bourgeois, 
then  we  are  as  far  from  understanding  the  word  as  ever  we  were." 

As  a  matter  of  teaching,  Madame  de  Coulevain  makes 
a  serious  mistake  in  the  sentence,  "Its  characteristics 
are  to  be  found  in  people  who  have  received  a  supe- 
rior culture,"  etc.  No  doubt  the  context  shows  that 
bourgeoisisme  is  to  be  found  elsewhere  than  among 
people  who  have  received  a  superior  culture.  But  the 
teacher  has  no  right  to  depend  entirely  upon  contexts, 
and  the  pupil  is  in  this  sentence  warranted  in  demand- 
ing the  caution  of  an  "even"  placed  before  the  words 
"hi  people  who  have,"  etc.  As  illustration,  Madame 
de  Coulevain's  effort  has  evidently  failed  so  far  as 
Miss  Stephens  is  concerned.  The  cause  of  the  trouble 
is  the  necessity  under  which  Madame  de  Coulevain 


296    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

labours  of  being  brilliant,  antithetical,  epigrammatic. 
It  would  have  been  quite  possible  for  her  to  select 
less  violent  contrasts  that  would  substantiate  the 
distinctions  implied  in  her  general  description  of 
bourgeoisisme. 

Often  elaboration  may  be  very  usefully  employed 
along  certain  clearly  defined  lines.  To  get  a  clear  idea 
of  something,  it  is  frequently  desirable  to  isolate  certain 
groups  of  ideas.  It  is  sometimes  worth  while  to  attend 
to  only  one  set  of  things  for  a  while,  to  the  exclusion  of 
certain  concomitants.  For  example,  it  might  be  use- 
ful to  select  from  all  the  available  biographies  what 
certain  men  of  a  particular  class  of  genius  were  en- 
gaged with  at  a  certain  fixed  age,  say  25.  It  is  a  capital 
exercise  to  make  a  class  discover  what  was  occupying  the 
attention  of  ten  selected  poets,  or  generals,  or  states- 
men, or  men  of  science  at  this  age.  A  particularly 
interesting  exercise  is  to  make  the  age  coincide  with  that 
of  the  pupil,  and  put  the  exercise  in  the  form:  What 
were  the  following  distinguished  men  occupied  with  and 
interested  in  at  your  own  age?  The  difficulty  is  no 
doubt  to  get  accurate  and  full  details  of  the  earlier 
years  of  important  men.  But  great  ingenuity  is  often 
shown  by  pupils  in  interpreting  in  terms  of  their  own 
experience  the  scanty  materials  found  in  biographies. 
We  have  here,  in  fact,  an  excellent  illustration  of  the 
process  of  elaboration  guided  by  the  subjective  feeling 
of  the  pupil. 


CHAPTER  XII 

DEGKEE  IN  ILLUSTRATION 

IN  a  general  way  we  must  distinguish  between  the 
quantitative  and  the  qualitative  in  Illustration.  It 
may  be  possible  to  illustrate  a  certain  fact  or  relation 
without  having  to  go  into  quantitative  details.  There 
are  some  matters  that  we  either  understand  or  we  do  not 
understand.  The  meaning  of  such  conceptions  as  size, 
cause,  number,  intensity,  may  be  clearly  conveyed  and 
intelligibly  illustrated  in  the  course  of  ordinary  exposi- 
tion, without  any  undue  strain  on  the  part  of  the  pupil. 
A  general  knowledge  of  any  of  these  conceptions  may  be 
gathered  from  a  comparatively  small  number  of  cases. 
No  doubt,  in  order  to  enrich  the  conceptions,  it  is  neces- 
sary to  multiply  examples,  but  the  nature  of  the  con- 
ceptions does  not  change,  however  great  the  number  of 
examples  adduced.  The  idea  of  number  as  number, 
and  of  size  as  size,  remains  the  same,  no  matter  what  the 
nature  of  the  phenomena  may  be  hi  connection  with 
which  number  and  size  are  studied.  But  a  pupil  may 
be  able  to  understand  very  clearly  what  size  and  number 
are,  and  yet  may  be  unable  to  realise  the  meaning  of 
certain  sizes  and  numbers.  It  is  one  thing  to  understand 
the  general  meaning  of  a  term,  it  is  quite  another  to 
appreciate  intelligently  the  degrees  that  may  be  in- 
cluded within  the  scope  of  that  term.  The  pupil  may 
have  quite  a  clear  mastery  of  the  meaning  of  number, 

297 


298    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

and  yet  may  have  no  real  command  over  the  concept  of 
a  million.  In  these  days  of  millionaires  and  multi- 
millionaires it  may  be  a  little  easier  to  attach  a  definite 
meaning  to  the  figures  1,000,000;  and  it  is  probable 
that  Ruskin,  in  the  following  passage,  underestimates  the 
percentage  of  people  who  know  the  meaning  of  a  million; 
but  there  is  enough  truth  in  it  to  make  it  worth  our 
attention:  — 

"In  our  exceeding  prudence  we  are,  at  this  moment,  refusing 
the  purchase  of,  perhaps,  the  most  interesting  picture  by  Raphael  in 
the  world,  and  certainly  one  of  the  most  beautiful  works  ever 
produced  by  the  art-wisdom  of  man,  for  five-and-twenty  thousand 
pounds,  while  we  are  debating  whether  we  shall  not  pay  three 
hundred  millions  to  the  Americans,  as  a  fine  for  selling  a  small  frig- 
ate to  Captain  Semmes.  Let  me  reduce  these  sums  from  thousands 
of  pounds  to  single  pounds ;  you  will  then  see  the  facts  more  clearly 
(there  is  not  one  person  in  a  million  who  knows  what  a  '  million ' 
means ;  and  that  is  one  reason  the  nation  is  always  ready  to  let  its 
ministers  spend  a  million  or  two  in  cannon,  if  they  can  show  that 
they  have  saved  twopence-halfpenny  in  tape).  These  are  the  facts, 
then,  stating  pounds  for  thousands  of  pounds;  you  are  offered  a 
'  Nativity '  by  Raphael,  for  five-and-twenty  pounds,  and  cannot 
afford  it ;  but  it  is  thought  you  may  be  bullied  into  paying  three 
hundred  thousand  pounds,  for  having  sold  a  ship  to  Captain 
Semmes."  * 

This  method  of  proportionate  reduction  is  certainly 
useful  in  giving  an  idea  of  relative  values,  but  it  in- 
troduces complications  of  its  own.  A  Raphael  at 
twenty-five  pounds  is  as  incongruous  as  a  fine  of  three 
hundred  millions  for  selling  a  ship.  Further,  when  the 
reduced  total  still  amounts  to  the  vast  sum  of  three 
hundred  thousand  pounds,  it  is  probable  that  all  who 
really  understand  this  quantity  would  also  have  an 

1  The  Eagle's  Nest,  Lecture  II. 


DEGREE  IN   ILLUSTRATION  299 

intelligent    mastery   of   the   concept    three   hundred 
millions. 

But  it  has  to  be  admitted  that  the  expositor  is  faced 
by  serious  difficulties  the  moment  he  introduces  the 
notion  of  degree.  The  pupil  is  found  to  be  able  to  use 
his  conceptions  only  within  certain  limits  determined 
by  his  range  of  experience.  When  asked  as  a  school 
exercise  to  write  a  letter  to  a  companion  telling  how  he 
spent  a  quarter  given  by  a  generous  uncle,  a  pupil  from 
a  poverty-struck  home  will  often  write  intelligently 
and  interestingly.  But  if  the  teacher  makes  the  imagi- 
nary uncle  prodigal  enough  to  present  a  ten-dollar  bill, 
the  result  on  the  composition  is  disastrous.  The  pupil 
cannot  rise  to  the  expenditure  of  such  a  vast  sum.  A 
quarter  is  a  real  thing  to  him,  a  coin  that  he  has  handled, 
a  sum  of  money  that  he  has  already  manipulated, 
though  perhaps  never  with  the  entirely  free  hand 
permitted  in  an  irresponsible  letter.  He  may  have  seen 
a  ten-dollar  bill,  and  is  certainly  able  to  tell  you  at  a 
moment's  notice  how  many  quarters  he  could  get  in 
exchange  for  it.  But  to  the  poor  boy  the  bill  is  some- 
thing beyond  the  range  of  everyday  operations.  It 
represents  capital  rather  than  cash,  and  in  consequence 
the  letter  usually  takes  the  form  of  various  recommenda- 
tions for  banking  the  troublesome  money,  or  at  any  rate 
making  some  economic  or  philanthropic  use  of  it.  A 
common  device  among  young  letter-writers  under  such 
trying  circumstances  is  to  describe  the  spending  of,  say, 
one  dollar  out  of  the  whole,  in  ways  that  appeal  to 
young  desires,  and  to  hand  over  the  remaining  nine  to 
mother,  who  is  so  badly  in  need  of  them.  A  boy  from  a 
wealthy  home,  if  asked  to  write  a  similar  letter  on  a  ten- 
dollar  basis,  finds  no  difficulty;  but  a  $1000  bill  gives 


300    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

him  pause.  Yet  while  the  difference  between  $10  and 
$1000  is  greater  than  that  between  a  quarter  and  $10, 
the  wealthy  boy  finds  less  difficulty  in  passing  from 
the  small  bill  to  the  big  one  than  his  poorer  fellow 
has  in  passing  from  the  quarter  to  the  small  bill. 
Accustomed  to  copious  supplies  of  pocket  money,  the 
rich  boy  is  less  impressed  by  $1000  than  the  poor  boy 
by  $10. 

In  relation  to  any  class  of  phenomena,  we  have  all 
different  thresholds  of  impressionability.  What  would 
astonish  a  farm-hand  in  New  York  would  make  no  im- 
pression on  a  seasoned  dweller  in  that  city;  while  the 
New  Yorker,  as  paying  guest  at  a  farm,  finds  himself 
impressed  by  many  things  that  leave  his  hosts  un- 
moved. In  any  department  we  must  have  stimuli  of 
a  certain  degree  of  intensity  before  we  are  impressed; 
this  intensity  may  be  increased  up  to  a  certain  point, 
but  when  this  point  is  reached,  we  pass  beyond  the 
upward  limit  of  impressionability. 

For  the  benefit  of  Shadrach,  Meshach,  and  Abednego, 
Nebuchadnezzar  "spake,  and  commanded  that  they 
should  heat  the  furnace  one  seven  times  more  than  it 
was  wont  to  be  heated. ' ' l  This  passage  worried  me  when 
I  was  a  boy.  To  me  a  furnace  was  a  furnace,  and  once 
it  had  been  properly  kindled  and  was  well  supplied  with 
fuel,  it  was  as  hot  as  it  could  be.  I  was  unable  to  under- 
stand how  it  could  be  hotter;  and  further,  even  if  it 
could,  I  was  at  a  loss  to  see  how  that  was  going  to 
benefit  Nebuchadnezzar.  As  soon  as  his  three  victims 
were  placed  in  the  furnace,  they  would  be  instantane- 
ously burnt  up.  I  could  not  conceive  of  degrees  of 
combustion.  A  man  was  either  burnt  up  or  he  was 

1  Daniel  iii.  19. 


DEGREE  IN  ILLUSTRATION  301 

not.  My  boyish  point  of  view  I  find  well  illustrated  in 
a  remark  made  by  Mr.  H.  G.  Wells  in  speaking  of  the 
wonders  of  Niagara.  He  is  not  greatly  impressed,  and 
says:  "A  hundred  tons  of  water  is  just  as  stunning  as 
ten  million.  A  hundred  tons  of  water  stuns  one  alto- 
gether, and  what  more  do  you  want  ?  " 1  ^1  could  not  un- 
derstand what  more  Nebuchadnezzar  wanted.  My  reli- 
gious instructor  informed  me  that  I  need  not  worry 
about  the  number  seven.  The  passage  had  no  arith- 
metical signification,  and  merely  meant  that  the  fur- 
nace was  heated  very  much  more  than  usual.  This 
was  no  doubt  quite  satisfactory  from  the  religious  stand- 
point, but  it  left  something  to  be  desired  in  other  direc- 
tions. Indeed,  it  was  not  till  I  had  come  across  certain 
figures  some  years  later  regarding  the  temperatures 
in  blast-furnaces  that  I  realised  that  there  might  be 
good  science  as  well  as  good  religion  in  the  story  found 
in  Daniel. 

It  is  true  that  the  figures  I  encountered  raised  fresh 
difficulties.  It  was  stated  in  the  text-book  that  at  the 
mouth  of  a  certain  blast-furnace  the  temperature  was 
320°  centigrade,  and  that  it  went  on  increasing  with  the 
depth,  till  at  a  distance  of  34  feet  from  the  mouth  the 
temperature  was  1450°  C.  This  enormous  tempera- 
ture was  clearly  far  beyond  my  Threshold  of  Stun. 
Between  zero  and  100°  C.  I  felt  that  I  not  only  under- 
stood but  realised  the  different  degrees  of  heat.  I  had 
experienced  the  heat  of  boiling  water,  and  ordinary 
childish  curiosity  had  given  me  a  fleeting  experience 
of  the  presumably  higher  temperature  of  red-hot  iron. 
I  was  quite  convinced  that  after  the  boiling  point  of 
water  I  had  no  clear  notion  of  what  increase  in  tempera- 

1  The  Future  in  America,  p.  72. 


302    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

ture  meant.  It  accordingly  conveyed  little  to  my  mind 
when  I  was  told  that  the  heat  at  the  bottom  of  a  blast- 
furnace is  so  great  that  it  must  be  measured  by  a  num- 
ber fourteen  and  a  half  times  as  great  as  that  which 
measures  the  heat  of  boiling  water.  Still,  as  experience 
brought  me  more  and  more  examples  of  very  high  tem- 
peratures used  in  actual  processes,  I  began  to  have  a 
working  knowledge  of  what  these  temperatures  may 
mean.  The  fusing  points  of  the  different  metals 
naturally  supply  figures  that  have  a  practical  value. 
When  the  pupil  is  told  that  pure  silver  fuses  at  960°  C., 
pure  gold  at  1075°  C.,  and  pure  platinum  at  1775°  C., 
he  begins  to  attach  a  meaning  to  those  high  tempera- 
tures. If,  now,  he  examines  the  table  of  fusion  points 
of  Prinsep's  Alloys  (the  silver  and  gold  series,  and  the 
gold  and  platinum  series),  he  gets  a  still  clearer  view  of 
the  meaning  of  relativity  of  temperature.  To  realise 
in  any  degree  the  still  higher  temperature  of  the  oxyhy- 
drogen  flame  (estimated  by  Bunsen  at  2844°  C.)  and 
the  electric  arc  (3000°  C.  to  3900  C.°),  the  pupil  must 
familiarize  himself  with  certain  processes  with  which 
these  are  connected. 

In  all  this  practical  application,  in  order  to  acquire  an 
intelligent  acquaintance  with  matters  entirely  beyond 
our  Threshold  of  Stun,  it  will  be  found  that  there  is  a 
natural  tendency  always  present  to  interpret  unrealis- 
able  quantities  in  terms  of  realisable.  For  example,  when 
the  pupil  is  told  the  various  temperatures  of  the  differ- 
ent parts  of  the  Bunsen  flame  —  outer  flame  1350°  C., 
violet  1250°  C.,  blue  1200°  C.,  central  dark  cone  from 
250°  to  650°  C.,  he  finds  that  he  has  a  sort  of  impression 
that  the  inner  dark  cone  is  comparatively  cool.  The 
very  introduction  of  this  term  cool  is  an  indication  of  a 


DEGREE  IN   ILLUSTRATION  303 

reference  to  a  subjective  instead  of  to  an  objective 
standard.  This  mixing  of  standards  is  to  be  avoided, 
except  in  cases  in  which  we  are  working  below  the 
Threshold  of  Stun.  The  moment  we  have  risen  above 
that  threshold  we  must  do  our  comparisons  in  terms 
of  units  that  may  have  been  originally  fixed  in  rela- 
tion to  something  within  our  subjective  experience, 
but  which,  once  we  have  passed  the  threshold,  can  no 
longer  be  tested  by  reference  to  that  experience. 

Without  making  any  pretence  of  severe  scientific 
accuracy  in  this  matter  of  stun,  we  may  help  our  think- 
ing by  using  some  of  our  terms  in  a  clearly  defined 
way.  Let  that  degree  of  intensity  of  stimulus  that  just 
rouses  our  attention  to  a  particular  fact  or  phenomenon 
mark  the  Threshold  of  Impressionability  to  that  class 
of  facts  or  phenomena.  All  the  range  between  this  and 
the  point  at  which  we  are  stunned  may  well  be  spoken 
of  as  the  Zone  of  Impressionability.  Above  the  Thresh- 
old of  Stun,  of  course,  is  the  region  where  nothing  mat- 
ters, so  far  as  direct  experience  goes. 

In  dealing  with  the  rich  and  poor  boy,  we  were  practi- 
cally working  all  the  time  within  the  Zone  of  Impres- 
sionability. Neither  of  the  boys  was  really  stunned. 
Each  of  them  found  himself  faced  by  a  certain  difficulty 
in  dealing  with  quantities  beyond  his  usual  scale;  but 
neither  was  brought  up  against  unintelligibility  as 
would  have  been  the  case  had  they  been  called  upon  to 
deal  with  millions  in  a  practical  way.  In  the  case  of 
temperatures  we  find  that  there  is  a  small  range  within 
which  heat  can  be  estimated  by  sensation,  but  above  and 
below  this  range  there  are  long  sweeps  of  gradations  of 
temperature  that  may  be  understood  and  intelligently 
applied,  but  that  cannot  be  interpreted  in  terms  of 


304    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

sensation.  In  estimating  the  climate  of  a  country  or 
the  heat  of  a  bath,  a  writer  may  depend  upon  his  readers 
making  subjective  references,  and  he  knows  within 
what  limits  he  can  depend  upon  not  exceeding  their 
Threshold  of  Stun.  But  in  all  temperatures  above 
and  below  the  points  at  which  the  human  organism 
ceases  to  record  gradation  there  is  no  meaning  in  refer- 
ring to  sensations  in  estimating  heat.  There  is  no  need 
that  we  should  have  a  physical  realisation  of  200°  C., 
not  to  mention  2400°  C. 

In  a  crude  physical  sense  we  may  treat  the  range 
within  which  the  bodily  organism  records  gradations  of 
temperature  as  the  zone  of  impressionability  to  heat. 
But  our  mental  impressionability  to  ideas  of  the 
gradations  of  heat  is  a  quite  different  matter.  Our 
physical  Threshold  of  Stun  is  reached  long  before  OUT 
mental.  Even  on  the  physical  basis  the  Threshold  of 
Stun  may  be  slightly  raised.  The  exact  number  of  tons 
of  water  that  would  stun  Mr.  Wells  at  Niagara  might 
not  be  enough  to  stun  him  at  a  later  stage  if  he  took  to 
living  close  by  a  waterfall  that  carried  just  the  requisite 
number  of  tons  to  stun  him  at  the  present  moment. 
By  and  by  it  would  be  necessary  to  increase  the  number 
of  tons  if  the  stunning  was  to  be  kept  up.  But  this 
raising  of  the  threshold  could  not  be  carried  very  far. 
A  point  is  soon  reached  beyond  which  the  stun  is  in- 
surmountable, and  indeed  this  higher  degree  of  stimulus 
would  probably  lead  to  the  permanent  injury  of  the 
organs  stimulated. 

On  the  mental  side,  however,  there  is  nothing  to 
hinder  the  gradual  but  steady  raising  of  the  Threshold  of 
Stun  with  regard  to  any  of  the  departments  of  the  activ- 
ity of  the  mind.  It  may  be  said  that  an  important  part 


DEGREE  IN  ILLUSTRATION  305 

of  a  teacher's  work  consists  in  the  raising  of  the  Thresh- 
old of  Stun,  a  little  on  the  sensational  plane,  and  a 
great  deal  on  the  intellectual.  It  is  his  business  to  use 
the  senses  and  the  ideas  so  as  to  provide  a  basis  on 
which  the  pupil  may  continue  to  build  in  such  a  way 
that  his  Threshold  of  Stun  shall  continue  rising  in 
those  matters  that  are  important  to  him.  There  is  no 
reason  for  this  raising  process  to  cease  till  physical 
decay  intervenes. 

In  the  matter  of  large  numbers  and  vast  distances, 
teachers  are  fully  alive  to  the  need  for  finding  means  to 
enable  the  pupil  to  realise  quantities  that  are  at  first 
quite  beyond  him.  The  usual  plan  adopted  is  to  in- 
stitute some  sort  of  comparison  between  small  and  great. 
In  particular  the  attempt  is  made  to  get  rid  of  the  unin- 
telligibility  of  vast  numbers  by  expressing  the  results 
of  some  process  of  manipulating  them.  The  following 
is  a  typical  attempt  to  get  people  to  realise  the  enor- 
mous distances  dealt  with  in  astronomy :  — 

"Let  us  suppose  a  railway  to  have  been  built  between  the  earth 
and  the  fixed  star  Alpha  Centauri.  By  a  consideration  of  this  rail- 
way's workings  we  can  get  some  idea  of  the  enormous  distance  that 
intervenes  between  Centaurus  and  us.  Suppose  that  I  should  de- 
cide to  take  a  trip  on  this  new  aerial  line  to  the  fixed  star.  I  ask 
the  ticket  agent  what  the  fare  is,  and  he  answers :  — 

"  '  The  fare  is  very  low,  sir.    It  is  only  a  cent  each  hundred  miles.' 

"  '  And  what,  at  that  rate,  will  the  through  ticket  one  way  cost  ? ' 
I  ask. 

" '  It  will  cost  just  $  3,750,000,000,'  he  answers. 

"  I  pay  for  my  ticket  and  board  the  train.  We  set  off  at  a  tre- 
mendous rate. 

"  '  How  fast  ? '  I  ask  the  brakeman, '  are  you  going  ? ' 

"  'Sixty  miles  an  hour,  sir,'  says  he,  'and  it's  a  through  train. 
There  are  no  stops.' 

"  'We'll  soon  be  there,  then,  shan't  we ? '  I  resume. 
x 


306    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

"  'Well  make  good  time,  sir/  says  the  brakeman. 
" '  And  when  shall  we  arrive  ? ' 
"  'In  just  48,663,000  years.'" 

—  Philadelphia  Bulletin.1 

The  enormous  fare  is  certainly  very  impressive,  but 
it  is  doubtful  whether  much  is  gained  by  representing 
the  distance  in  terms  of  money,  since  in  any  case  the 
numbers  are  clearly  beyond  the  Threshold  of  Stun.  No 
pupil  can  really  appreciate  the  meaning  of  three  and 
three-quarter  billions,  and  if  he  is  to  be  impressed  by  the 
mere  number  of  digits,  it  would  be  more  effective  to  tell 
hun  plainly  that  Alpha  Centauri  is  37,500,000,000,000 
miles  away.  As  a  matter  of  experience  I  found  that 
many  people  to  whom  this  illustration  was  presented  at 
once  proceeded  to  reduce  the  dollars  to  cents  and  then  to 
multiply  the  result  by  one  hundred  in  order  to  get  at  the 
exact  number  of  miles.  It  may  be  felt  that  at  any  rate 
the  forty-eight  million  years  will  help  the  pupil  to  realise 
the  enormous  distance.  But  the  time  is  so  great  that 
there  is  an  opportunity  for  the  mind  to  conceive  of  the 
journey  as  being  a  rather  restful  experience.  Instead 
of  being  impressed  by  the  enormous  space  passed  over, 
the  mind  is  inclined  to  dwell  upon  the  evenness  of  the 
journey.  So  far  as  the  illustration  appeals  to  the  picto- 
rial, it  defeats  the  ends  of  the  illustrator,  for  the  hurry 
and  bustle  of  the  train  disappear  when  we  project  it 
against  the  silence  of  limitless  space. 

It  is  interesting  to  compare  a  parallel  illustration  of 

1  Quoted  by  Mitchill  and  Carpenter :  Exposition  in  Class-room  Prac- 
tice, p.  231.  Those  who  accept  the  arithmetical  challenge  and  seek 
to  reconcile  the  dollar  calculation  with  the  result  in  years  will  find 
their  work  cut  out  for  them.  It  would  appear  that  in  cases  of  such 
vast  numbers  the  arithmetical  challenge  is  less  alluring  than  usual. 
The  reader  is  inclined  to  take  the  writer's  word  for  it. 


DEGREE   IN   ILLUSTRATION  307 

the  same  distance  as  found  in  Sir  Robert  Ball,  who  is  a 
master  in  such  matters.  He  begins  by  bluntly  stating 
the  distance,  which  he  says  may  be  expressed  in  miles 
by  a  2  followed  by  thirteen  ciphers.  Knowing  that  the 
expression  20,000,000,000,000  (which,  by  the  way,  does 
not  correspond  to  the  Bulletin's  figures  —  but  fortu- 
nately we  are  not  here  responsible  for  the  facts  that  we 
have  to  illustrate)  is  far  beyond  his  readers'  Threshold  of 
Stun,  he  sets  about  an  explanation *  that  is  an  admirable 
illustration  of  the  process  of  elaboration.  Like  the 
Bulletin,  Sir  Robert  arranges  for  a  special  tariff :  in  his 
case  a  penny  per  hundred  miles.  Then  taking  the 
British  National  Debt,  which  at  that  time  (April,  1887) 
amounted  to  £736,000,000,  he  seeks  to  make  his  readers 
realise  this  vast  sum  by  first  of  all  pointing  out  that  the 
mere  interest  at  a  low  rate  amounts  to  £60,000  per  day. 
Then  he  imagines  the  youngster  filling  his  pockets 
with  gold  so  as  to  go  and  buy  a  ticket.  Pockets  failing, 
a  cart  has  to  be  called  in:  ten  carts,  fifty  carts,  a  hun- 
dred carts.  Finally,  the  young  traveller  starts  at  the 
head  of  his  procession  of  five  thousand  carts  of  gold,2 
only  to  find  that,  so  far  from  getting  any  change  back, 
he  is  still  more  than  £100,000,000  short  of  the  specially 
reduced  fare. 

Approaching  the  matter  anew  from  a  different  point, 
Sir  Robert  gives  some  figures  regarding  the  number  of 
miles  of  cotton  yarn  produced  in  a  Lancashire  mill,  then 
in  all  the  Lancashire  mills.  Finally,  he  works  up  to  the 

1  Starland,  p.  317.     The  book  is  a  popular  Exposition  intended  for 
young  readers. 

2  On  a  calculation  on  the  basis  of  3|  sovereigns  to  one  ounce  avoir- 
dupois, it  would  not  appear  that  each  cart  was  overladen.     Yet  263 
pounds  demand  a  vehicle  of  some  sort,  so  the  illustration  may  be  jus- 
tified. 


308    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

statement  that  400  years  would  be  necessary  for  enough 
cotton  to  be  grown  in  America  and  spun  in  England 
before  there  would  be  enough  thread  to  reach  to  the 
nearest  fixed  star.  But  the  highest  point  is  reached 
when  he  says  that  "All  the  spinning  that  has  ever  yet 
been  done  in  the  world  has  not  produced  a  long  enough 
thread"  to  reach  from  the  earth  to  the  nearest  fixed 
star.  This  spinning  illustration  I  find  causes  too  many 
questions  to  be  asked  as  to  details.  Are  the  American 
mills  included,  or  must  all  the  spinning  be  done  in 
England  ?  —  and  so  forth.  Illustrations  should  not 
challenge  such  queries. 

Sir  Robert's  illustration  from  the  fact  that  from 
certain  of  the  fixed  stars,  in  spite  of  the  enormous 
velocity  of  light,  it  would  be  possible  at  the  present 
moment  to  see  the  Battle  of  Waterloo  going  on,  is 
damaged  by  the  pathetic  condition,  if  the  inhabitants 
"had  good  enough  telescopes."  Strangely  enough,  this 
if  is  a  much  greater  stumbling-block  to  pupils  than  that 
in  the  other  illustration,  that  if  a  telegraphic  message 
had  been  sent  off  at  the  time  to  announce  the  birth  of 
our  Lord,  it  would  be  still  on  its  way  to  some  of  the 
remoter  fixed  stars.  In  all  this  we  are  quite  beyond  the 
Threshold  of  Stun,  and  the  materials  of  our  illustration 
are  tested  more  from  the  terrestrial  than  the  celestial 
point  of  view.  Somehow  my  students  almost  unani- 
mously confess  to  be  much  more  impressed  by  the  tele- 
gram illustration  than  by  all  the  others,  though  several 
have  said  that  they  enjoyed  lingering  over  the  possibili- 
ties of  what  could  be  seen  from  appropriate  stars. 
Here  we  have  the  illustration  becoming  the  substantive 
matter  of  thought. 

The  change  from  the  railway  unit  to  the  telegraphic 


DEGREE   IN   ILLUSTRATION  309 

certainly  increases  the  general  impression  of  enormous 
distances.  If  we  go  on  multiplying  examples,  we  do 
gradually  get  a  notion  of  the  relativity  involved.  But 
the  only  way  in  which  we  can  realise  vast  quantities 
is  by  manipulating  them,  and  utilising  the  conception 
of  relativity  so  as  to  reach  certain  practical  conclusions 
respecting  the  matter  actually  involved.  When  the 
astronomer  tells  us  that  Sirius  is  1,375,000  times  farther 
away  from  us  than  the  sun  is,  we  take  the  gentleman's 
word  for  it;  but  we  do  not  realise  what  he  means.  It  is 
true  that  some  of  us  would  accept  the  arithmetical 
challenge  implied  in  his  statement  and  work  out  the 
equation :  — 

93,000,000  x  1,375,000  =  127,875,000,000,000 

and  some  of  us  might  derive  satisfaction  from  being 
able  to  say  that  Sirius  is  one  hundred  and  twenty-seven 
trillion  eight  hundred  and  seventy-five  billion  miles 
from  the  earth;  but  are  we  any  farther  forward  as  to 
what  it  all  means  ?  The  answer  is  to  be  found  in  the 
fact  that  we  can  manipulate  these  figures  in  an  intelli- 
gent way.  We  can  make  calculations  and  come  to 
certain  conclusions  based  on  them,  conclusions,  be  it 
observed,  that  a  plain  man  can  come  to  on  his  own 
account  when  the  matter  is  properly  presented  to  him. 
The  following  is  taken  from  a  school  text-book  that  was 
formerly  very  widely  used  and  in  which  a  small  section 
is  set  apart  for  purely  astronomical  matters :  — 

"It  has  been  calculated  that  if  the  sun  were  removed  to  the 
distance  of  Sirius,  it  would  shine  with  only  T^T  part  of  its  lustre, 
and  it  has  been  conjectured,  therefore,  that  the  diameter  of  Sirius 
must  be  at  least  twelve  times  greater  than  that  of  the  sun.  Of  this, 
however,  we  cannot  be  certain,  for  spectrum  analysis  has  taught  us, 
among  other  things,  that  stars  shine  with  different  degrees  of  bright- 


310    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

ness,  owing  probably  to  differences  of  temperature,  and  that  Sirius 
is  among  the  hottest  and  brightest  of  all."  ' 

We  have  here  a  calculation  —  not  a  very  safe  one,  as 
the  writer  warns  us,  but  quite  an  intelligible  one  — 
based  upon  the  enormous  distance  that  we  admit  we 
cannot  realise.  The  calculation  is  none  the  less  valid. 
Further,  when  we  begin  to  compare  one  fixed  star 
with  another,  and  to  arrange  the  stars  into  their  various 
magnitudes,  we  gradually  begin  to  attach  a  more  or 
less  definite  meaning  to  the  enormous  astronomical 
numbers:  we  can  behave  intelligently  towards  them. 
So  with  the  minute  subdivisions  implied  in  the  atomic 
theory,  and  the  newer  theories  that  appear  to  demand 
an  even  minuter  subdivision.  Chemists  can  act  intelli- 
gently upon  certain  calculations  based  on  units  that  they 
cannot  realise. 

The  following  illustration  was  burned  into  my  mind 
at  a  very  early  period.  It  occurs  in  the  geography 
text-book  2  on  which  I  was  brought  up :  — 

"The  distance  from  Liverpool  to  New  York  is  about  3500  miles, 
and  can  be  traversed  in  about  10  days.    At  this  rate  the  time  re- 
quired to  go  from  the  Sun  to  the  planets  would  be  as  follows : — 
289  years  to  Mercury. 
540  years  to  Venus. 
744  years  to  Earth. 
1,127  years  to  Mars. 
1,720  years  to  the  nearer  Asteroids. 
2,372  years  to  the  more  distant  Asteroids. 
3,867  years  to  Jupiter. 
7,092  years  to  Saturn. 
14,262  years  to  Uranus. 
22,521  years  to  Neptune. 
156,500,000  years  to  nearest  fixed  star. 

1  William  Lawson  :  Outlines  of  Physiography,  p.  249. 

3  Modern  Geography  for  the  Use  of  Schools,  by  Robert  Anderson. 


DEGREE  IN   ILLUSTRATION  311 

"  At  this  rate  it  would  have  taken  from  1000  years  before  the 
creation  of  man  till  now,  in  order  to  reach  even  Saturn." 

This  old  illustration  is  not  introduced  for  its  own  sake, 
but  because  of  the  effect  it  produced  on  certain  students 
to  whom  it  was  presented.  Their  attitude  was  at  once 
that  of  the  superior  person.  They  did  not  quote 
Moliere,  but  they  led  me  clearly  to  understand  that  we 
had  now  changed  all  that,  and  that  thanks  to  the 
Mauretania  and  her  rivals  we  could  now  cut  down  these 
distances  by  exactly  one-half.  So  difficult  is  it  to  keep 
the  relative  and  the  absolute  in  their  proper  places. 
To  be  sure,  the  young  men  immediately  saw  their  error, 
and  one  of  them  justified  himself  to  some  extent  by 
saying  that,  after  all,  America  is  really  nearer  to  Europe 
than  it  was  last  century;  and  to  gainsay  him  was  not 
the  part  of  one  who  teaches  that  the  true  meaning  of  an 
idea  is  the  power  to  behave  intelligently  in  relation  to 
the  content  of  the  outer  world  involved  in  that  idea. 

Two  summers  ago  at  Niagara  I  read  one  of  those  folder 
advertisements  of  which  such  effective  use  is  made  in  the 
States.  Its  purpose  was  to  enhance  the  wonders  of 
the  falls.  The  length,  breadth,  thickness,  and  weight  of 
the  body  of  water  were  given,  and  after  the  mind  had 
been  sufficiently  harrowed,  the  climax  was  reached  by  a 
statement  of  the  length  of  time  that  it  took  for  a  cubic 
mile  of  water  to  fall  over.  I  do  not  remember  the  exact 
figures  of  the  folder,  but  have  a  vivid  recollection  of  the 
sense  of  anticlimax  involved.  On  calculating  out  the 
whole  matter,  I  find  the  effect  even  more  flattening  than 
my  memory  led  me  to  expect.  Taking  the  figures 
supplied  in  the  ninth  edition  of  the  Encyclopaedia 
Britannica  (these  are  old  enough  not  to  allow  for  any 
diversion  of  water  for  the  power  stations,  and  thus 


312    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

give  the  falls  a  fair  chance  to  show  up  well),  I  find  that 
18,000,000  cubic  feet  of  water  fall  over  every  minute. 
This  is  sufficiently  impressive,  but  when  worked  out 
on  a  volumetric  basis  the  best  we  can  say  for  the  falls 
is  that  they  toss  over  an  entire  cubic  mile  in  five  days 
sixteen  hours.1  The  impressiveness  gained  by  using 
the  magnificent  unit  of  one  cubic  mile  is  not  nearly 
sufficient  to  counterbalance  the  enormous  loss  in  actual 
digits. 

Few  people  are  able  to  realise  what  a  cubic  mile 
means.  In  fact,  the  calculation  we  have  just  made  has 
enabled  us  to  understand  better  what  is  implied  in  the 
higher  unit,  and  so  far  is  of  use.  But  the  question  we 
are  at  present  considering  is  the  illustrative  value  of 
the  cubic  mile  unit,  not  the  possibility  of  realising  that 
unit.  In  point  of  fact,  we  have  here  reversed  the  parts 
played  by  the  illustration  and  the  illustrandum.  The 

1  A  little  personal  experience  is  perhaps  in  order  here:  at  any 
rate,  it  is  instructive.  In  a  lecture  before  the  College  of  Preceptors 
in  London  in  May,  1909,  I  used  this  illustration,  but  I  made  a  mis- 
calculation to  the  extent  of  misplacing  a  decimal  point.  Though  my 
result  was  thus  ten  times  less  than  it  should  have  been,  it  seemed 
big  enough  to  correspond  to  what  I  remembered  from  the  folder,  so 
my  suspicions  were  not  aroused.  In  the  correct  verbatim  report  in 
the  Educational  Times  for  June  1  appears  the  passage:  "The  best 
we  can  do  is  to  say  that  in  thirteen  and  a  half  hours  a  whole  cubic  mile 
of  water  tumbles  over  the  cliffs."  No  one  wrote  to  correct  this  serious 
blunder:  but  I  am  not  now  surprised  that  the  usually  vigilant  arith- 
matician  forgot  his  customary  lust  for  accuracy.  Not  that  the  state- 
ment remained  unchallenged.  Without  troubling  to  work  out  details, 
an  acquaintance  —  an  astronomer  of  all  men  —  said  there  must  be 
something  wrong,  as  it  certainly  could  not  take  so  long  as  thirteen  and 
a  half  hours  for  a  cubic  mile  of  water  to  tumble  over  the  cliffs;  he 
had  seen  the  falls  and  he  knew.  It  was  because  of  his  objection 
that  I  revised  my  calculation,  and  now  I  find  it  very  hard  to  get  any- 
body to  believe  my  result  —  so  universal  is  the  inability  to  realise 
what  a  cubic  mile  actually  means. 


DEGREE  IN   ILLUSTRATION  313 

effect  of  the  present  paragraph  has  been  to  illustrate  the 
enormous  bulk  of  a  cubic  mile  by  means  of  the  Falls  of 
Niagara.  If  it  takes  even  these  gigantic  falls  five 
days  sixteen  hours  to  hurl  over  one  cubic  mile  of  water, 
then  we  may  have  some  idea  of  what  this  unit  implies. 

To  obtain  a  pictorial  conception  of  a  cubic  mile  is  not 
only  difficult,  but  is  of  doubtful  utility.  In  climbing  an 
Alp  we  may  be  fortunate  enough  to  come  across  a  preci- 
pice that  is  just  about  a  mile  deep,  and  has  certain  rela- 
tions with  neighbouring  landmarks  that  enable  us  to 
separate  out  approximately  a  cubic  mile  of  air-filled 
space.  The  effect  is  almost  always  disappointing. 
The  mile  seems  much  smaller  than  we  had  expected,  for 
the  obvious  reason  that  under  the  conditions  sketched 
the  surroundings  are  on  such  a  grand  scale  that  the 
imaged  mile  is  dwarfed  by  its  environment.  Some 
prefer  to  get  their  conception  through  the  medium  of 
water.  By  noting  certain  distances  on  shore,  and  by 
fixing  certain  marks  at  sea,  they  get  a  square  mile 
marked  out,  and  then  proceed  to  overwork  their  imagi- 
nation in  an  attempt  to  figure  out  the  cube  of  water  of 
which  the  marked  square  mile  is  the  upper  face.  The 
important  point,  however,  is  not  to  make  a  picture  of  a 
cubic  mile,  but  to  realise  by  practical  applications  what 
it  actually  means. 

Many  illustrations  aim  at  the  pictorial  when  they 
should  really  seek  to  eliminate  it.  The  pupil  is  told 
that  there  are  approximately  sixteen  hundred  million 
human  beings  at  present  living  upon  the  earth.  It  is 
difficult  to  realise  this  vast  number,  so  the  illustrator 
sets  about  making  a  picture.  He  selects  some  particu- 
lar part  of  the  world  that  will  just  hold  all  the  inhabit- 
ants of  the  earth  standing  packed  together.  The  best 


314    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

situation  is  obviously  an  island,  because  the  imagination 
will  have  the  aid  of  the  sea  in  limiting  its  operations. 
It  is  well  that  the  island  selected  should  have  some 
hill  from  the  top  of  which  the  whole  island  can  be 
envisaged.  The  Isle  of  Wight  in  the  south  of  England 
fulfils  this  condition  almost  perfectly.  Standing  on 
Ashey  Down,  the  spectator  can  command  the  whole 
island  with  a  very  trifling  exception.  The  illustrator 
now  proceeds  with  his  calculations.  The  island  covers 
about  147  square  miles,  and  each  square  mile  contains 
27,878,400  square  feet.  Accordingly,  the  island  in- 
cludes 4,098,124,800  square  feet.  This,  divided  by 
1,600,000,000,  gives  2.56  square  feet  per  human  being, 
or  a  square  of  about  19  in.  side  —  just  standing-room. 
Having  now  gathered  the  whole  human  race  on  the 
Isle  of  Wight,  what  better  off  are  we?  So  far  from 
being  helped,  the  imagination  is  harassed.  It  has  to 
work  overtime,  there  are  so  many  things  for  it  to  do 
with  this  huge  crowd.  The  scene  calls  up  too  many 
irrelevant  elements;  we  falter  in  our  attempts  to  realise 
the  different  sizes,  colours,  and  odours  of  those  people 
swept  in  from  all  ends  of  the  earth.  How  are  they  to  be 
fed  ?  Are  we  to  picture  them  as  arranged  by  nations  or 
indiscriminately  ?  How  could  they  stand  on  some  of  the 
steep  places  in  the  island  ?  I  have  seen  many  a  class 
reduced  to  desperation  by  the  surging  questions  raised 
by  this  preposterous  picture.  As  a  preliminary  to  a 
word-picture  of  the  Day  of  Judgment,  the  scheme 
may  have  its  advantages,  but  for  giving  an  idea  of  the 
population  of  the  world  it  is  not  very  successful.  In 
actual  practice  it  conveys  the  general  impression  that 
there  are  not  so  many  people  in  the  world  after  all. 
England  itself  is  not  very  big,  but  the  Isle  of  Wight  is 


DEGREE  IN  ILLUSTRATION  315 

such  a  little  place.  If  the  purpose  is  to  show  how 
much  room  there  is  still  in  the  world,  the  illustration 
is  effective  enough,  though  it  could  hardly  be  used  as  a 
fair  argument. 

The  best  appeal  is  always  to  the  highest  unit  available 
in  the  experience  of  the  persons  concerned.  Taking 
the  biggest  city  with  which  the  pupil  has  personal  ac- 
quaintance, this  could  be  compared  quantitatively 
with  the  number  of  people  in  the  pupil's  native  country, 
and  then  with  the  world  population.  The  United 
States  has  a  population  that  is  rapidly  approaching  the 
good-natured  number  100,000,000,  so  the  American 
boy  will  soon  have  the  advantage  of  a  ready-made  stand- 
ard that  renders  comparison  very  easy.  It  does  not 
follow  that  the  American  boy  realises  what  the  popula- 
tion of  his  republic  means.  Yet  all  that  is  necessary  for 
intelligent  comparison  is  present. 

We  need  a  standard  unit  for  our  illustrative  work,  but 
it  is  not  always  necessary  to  reduce  our  quantitative 
illustrations  to  this  standard  unit.  It  is  enough  if  we 
have  a  unit  to  which  we  can  reduce  them  all,  if  that  be 
necessary.  We  ought  to  have  a  clear  idea  of  what  one 
square  foot  means,  an  acre,  and  if  possible,  a  square 
mile.  In  certain  towns  the  municipal  authorities  are 
good  enough  to  lay  out  somewhere  hi  their  parks  a 
square  acre,  so  that  the  children  of  the  town  may  grow 
up  accustomed  to  this  as  a  standard.  The  Bank  of 
England,  in  London,  we  are  told,  covers  exactly  one 
acre  of  ground,  but  this  is  not  nearly  so  useful  a  standard 
as  the  square  acre.  The  bigger  the  quantities  we  are 
to  deal  with,  naturally  the  bigger  the  standard  unit. 
With  certain  astronomical  measurements  the  unit  is 
the  radius  of  the  earth,  with  others  the  diameter  of  the 


316    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

moon's  orbit,  with  still  others  the  major  axis  of  the 
earth's  orbit.  Whatever  the  standard,  it  must  be  a 
definite  one.  The  ordinary  householder  is  so  perplexed 
at  the  unintelligible  order  to  put  one  fluid  ounce  of 
pepsin  in  a  quart  of  milk  that  he  welcomes  the  prac- 
ticable if  inexact  equivalent  of  two  tablespoonfuls. 
But  in  deliberate  illustration,  some  sort  of  standard 
should  be  insisted  on,  and  should  not  be  changed  in  the 
process  of  Exposition  or  Illustration.  In  working  with 
money  values,  for  example,  we  may  have  occasion  to 
deal  in  several  different  coinages;  but  it  is  always  better 
to  keep  to  one  as  the  standard  during  any  one  series 
of  calculations.  Dollars  are  easily  valued  in  pounds 
sterling  as  we  go  along,  without  any  great  inaccuracy; 
but  there  is  a  great  deal  of  time  wasted  and  a  certain 
danger  of  confusion  incurred  by  continually  passing 
from  the  one  to  the  other.  Some  tourists  on  the  Conti- 
nent of  Europe  make  life  a  burden  to  their  friends  by 
dividing  by  eight  and  multiplying  by  five  at  every  kilo- 
metre stone.  In  a  kilometre  country  we  should  accept 
the  1000-metre  standard.  After  tramping  for  a  day  or 
two,  "32  kilometres"  is  as  clear  a  conception  as  is 
"20  miles"  at  home.  Of  course  where  actual  contrast 
between  the  two  standards  is  the  immediate  purpose, 
there  must  be  continual  interpretation  of  one  in  terms 
of  the  other.  But  in  most  cases  there  is  no  need  for  a 
double  standard,  and  usually  one  or  other  is  marked 
out  as  naturally  more  suited  for  the  particular  bit  of 
Exposition  in  hand  —  dollars  in  the  United  States,  kilo- 
metres in  France;  inches  in  a  popular  description,  centi- 
metres in  a  scientific  analysis. 


CHAPTER  XIII 

MATERIAL  ILLUSTRATIONS 

WHEN  we  try  to  classify  illustrations,  we  encounter 
certain  difficulties.  The  first  broad  distinction  that 
suggests  itself  among  the  various  kinds  of  illustration  is 
that  between  the  real  and  the  verbal.  There  seems  a 
very  important  difference  between  mere  words  on  the 
one  hand,  and  such  aids  as  objects,  models,  and  draw- 
ings on  the  other.  But  while  the  distinction  has  a  cer- 
tain convenience,  it  must  be  remembered  that  both 
real  and  verbal  illustrations  make  their  appeal  primarily 
to  the  same  set  of  forces :  the  only  way  they  can  get  at 
the  mind  is  by  rousing  ideas.  But  an  idea  may  be 
called  up  by  a  word  as  well  as  by  an  actual  object,  so 
that  the  two  kinds  of  illustrations  are  practically  one  on 
the  psychological  side.  There  is  the  more  need  to  insist 
upon  this  because  of  a  very  general  impression  among 
teachers  and  others  that  there  is  an  inherent  superi- 
ority in  things  as  compared  with  mere  words  as  a  means 
of  illustration.  But  here,  as  elsewhere,  "each  thing  in 
its  place  is  best."  It  has  to  be  remembered  that  verbal 
illustration  has  certain  advantages.  It  is  much  freer 
than  illustration  by  means  of  actual  objects:  it  gives 
much  more  scope  for  the  action  of  the  mind  appealed  to, 
since  in  any  case  only  the  content  already  acquired  can 
be  used.  The  clergyman  who  produces  an  actual  lily 
in  the  pulpit  to  illustrate  his  sermon  on  purity  thinks  he 

317 


318    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

has  used  a  stronger  illustration  than  if  he  had  merely 
referred  to  the  flower.  All  that  has  happened  is  that 
he  has  aroused  a  certain  amount  of  extrinsic  interest 
that  he  must  be  exceedingly  careful  to  turn  into  in- 
trinsic interest  hi  his  subject  before  he  can  hope  to  profit 
by  it  as  an  illustration.  The  children  can  take  out  of  the 
lily  only  what  they  were  able  to  put  into  it  before  it 
appeared  in  the  pulpit.  Anything  the  clergyman  can 
tell  them  about  the  lily  as  a  plant  will  no  doubt  increase 
the  knowledge  of  some  of  the  children.  But  this  is  the 
result  of  information  rather  than  of  illustration.  If  the 
clergyman  were  dealing  with  botany,  the  relation  be- 
tween the  lily  and  his  subject  would  be  different. 

We  must  clearly  distinguish  at  this  stage  between  an 
object  as  a  subject  of  study  and  as  an  illustration.  When 
we  are  giving  instruction  on  some  actual  object,  say  in 
chemistry,  botany,  or  geology,  nothing  can  make  up 
for  the  absence  of  that  object.  People  are  now  agreed 
that  in  practical  subjects  we  must  depend  upon  practi- 
cal work.1  Nothing  can  make  up  for  the  lack  of  labora- 
tory and  field  work.  Text-book  teaching  of  practical 
subjects  is  now  universally  condemned.  But  this 

1  This  is  the  general  view ;  but  there  are  dissentients.  Mr.  H.  W.  Eve, 
an  emeritus  headmaster  and  distinguished  physicist,  told  me  the  other 
day  that  there  was  no  need  for  the  pupil  to  do  the  experiments:  all 
that  was  necessary  was  that  he  should  understand  a  description  of 
them.  Sir  William  Ramsay  says,  "Far  too  much  stress  is  laid,  now- 
adays, on  what  is  called  'practical  work.'  It  is  possible  to  have 
quite  an  intelligent  idea  of  chemistry  without  ever  having  handled 
a  test-tube  or  touched  a  balance.  Lectures  on  chemistry  may  be  well 
illustrated  experimentally,  and  the  necessary  theories  demonstrated 
by  the  lecturer.  ...  To  spend  several  hours  a  day  in  practical  work 
is,  if  not  a  waste,  often,  at  least,  a  work  of  supererogation. "  Quoted 
by  Dr.  F.  H.  Hay  ward  in  his  stimulating  book,  The  Meaning  of  Edu- 
cation (p.  15). 


MATERIAL  ILLUSTRATIONS  319 

does  not  at  all  imply  that  a  test-tube  is  inherently  a 
better  illustration  than  a  metaphor.  In  the  mind  of 
the  teacher  there  is  too  often  a  sort  of  descending  scale 
of  merit  in  which  possible  illustrations  are  arranged 
somewhat  in  this  way :  — 

(1)  The  real  object,  for  which  anything  else  is  a 
more  or  less  inefficient  substitute. 

(2)  A  model  of  the  real  object. 

(3)  A  picture  of  the  object. 

(4)  A  diagram  dealing  with  some  of  the  aspects  of  the 
object. 

(5)  A  mere  verbal  description  of  the  object. 

Assuming  that  the  teacher's  purpose  is  to  give  infor- 
mation on  the  object,  the  above  order  of  merit  may  to  a 
large  extent  be  justified.  But  it  should  not  be  forgot- 
ten that  under  these  circumstances  we  are  dealing  with 
information  and  not  with  illustration.  Too  frequently 
the  above  general  order  of  merit  is  carried  over  to  the 
purely  illustrative  field,  and  we  have  an  unwarrantable 
glorification  of  "objects." 

Even  with  regard  to  what  is  properly  called  instruc- 
tion on  a  given  real  object,  there  are  certain  respects 
in  which  a  model  or  a  picture  may  be  actually  of  more 
service  than  the  thing  itself.  It  has  to  be  admitted 
that  it  is  not  always  possible  to  present  to  the  pupils 
the  real  thing.  In  all  cases  this  is  to  be  regretted.  It  is 
a  pity  that  such  things  as  Magna  Charta,  an  elephant,  a 
locomotive,  the  Port  of  Bordeaux,  cannot  be  brought 
to  school.  The  teacher  has  reluctantly  to  do  without 
them,  unless  he  is  able  to  take  his  class  where  these  things 
may  be  seen.  With  this  desire  for  the  real  we  must  all 
sympathise.  But  it  is  worth  while  noting  that  there 
are  certain  stages  in  instruction  when  a  model  is  not 


320    EXPOSITION  AND   ILLUSTRATION  IN  TEACHING 

only  as  good  as,  but  better  than,  the  object  it  represents. 
In  other  words,  the  model  actually  illustrates  the  real 
object.  Sometimes  the  object  is  too  large  to  be  taken 
in  at  one  sweep  of  the  eye,  and  is  therefore  difficult  to 
deal  with.  A  large  and  complicated  machine — take,  for 
example,  a  certain  paper-making  machine  that  as  a 
matter  of  fact  covers  an  area  of  over  two  thousand 
square  feet  —  may  be  far  better  understood  from  a 
small  working  model  than  from  the  machine  itself.  So 
with  extremely  small  objects  it  is  sometimes  very  desir- 
able to  have  a  magnified  model  for  illustrative  purposes. 
It  is  obvious  that,  in  using  a  model,  abstraction  must 
be  made:  the  model  must  lose  some  of  the  qualities 
that  belong  to  the  real  object.  Sometimes  the  ab- 
straction is  confined  to  size.  The  model  resembles  the 
original  in  every  respect  except  that  it  is  either  larger 
or  smaller.  A  model  locomotive  may  be  an  exact  re- 
production of  one  in  actual  operation  on  a  railway. 
On  the  other  hand,  it  may  be  slightly  changed  in  certain 
details  and  yet  convey  the  general  impression  of  being 
the  same  as  the  real  locomotive;  and  the  internal  va- 
riations may  increase  in  amount,  each  new  variation 
marking  a  higher  degree  of  abstraction.  For  example, 
the  model  may  have  exactly  the  same  machinery  as 
the  original,  but  the  heat  may  be  produced  by  burn- 
ing methylated  spirits  instead  of  coal ;  and  there  are 
obviously  all  the  degrees  of  increasing  abstraction 
till  we  reach  the  child's  toy  that  preserves  the  outward 
show,  but  is  worked  within  by  a  spring.  A  model  at  any 
of  these  grades  of  abstractness  may  have  its  use  as 
illustration,  everything  depending  on  the  nature  of  the 
illustrandum.  For  the  student  of  engineering  the 
model  must  be  so  accurate  that  he  can  make  from  it 


MATERIAL  ILLUSTRATIONS  321 

measurements  to  scale.  On  the  other  hand,  in  teach- 
ing mechanics,  a  clockwork  locomotive  is  quite  good 
enough  to  illustrate  certain  problems  of  gradients. 

In  the  case  of  students  studying  "in  the  field"  the 
structure  of  a  district  of  country,  say  the  Great  Lake 
area  in  the  St.  Lawrence  basin,  it  is  found  to  be  very 
difficult  for  them  to  have  a  grasp  of  the  whole  situation. 
They  can  see  now  this  part  and  now  that,  but  they  cannot 
from  any  one  point  envisage  the  whole.  Accordingly, 
they  are  set  to  make  a  relief  map  of  the  district  in  clay 
or  plasticine.  This  is  really  a  model  of  a  high  degree  of 
abstractness.  To  begin  with,  it  must  be  so  accurately 
worked  that  calculations  may  be  based  on  it,  allowance 
being  made  for  the  difference  between  the  horizontal 
and  the  vertical  scale.  But  the  only  real  points  of 
resemblance  between  the  model  and  the  district  are  in 
the  proportions  of  the  dimensions.  The  material  used 
is  of  no  consequence.  Of  course  in  a  more  elaborate 
scheme  the  different  strata  might  be  represented  by 
layers  of  different  coloured  clay  contorted  so  as  to  rep- 
resent the  actual  formations.  Sometimes,  indeed,  very 
elaborate  models  of  this  kind  are  made  in  glass,  so  that 
the  pupil  may,  from  the  side  of  the  case,  observe  the 
various  dips  of  the  strata,  and  note  the  faults.  But 
even  here  the  material  is  not  significant  of  the  illus- 
trandum. 

In  the  case  of  a  model  to  represent  that  bridge  over 
the  Rhine  that  has  given  so  much  trouble  to  every 
teacher  who  has  piloted  a  class  through  Caesar's  Com- 
mentaries,1 it  would  appear  to  be  possible  to  make  the 
model  correspond  to  the  original  in  all  the  respects  with 
which  we  are  acquainted.  While  such  a  model,  made 

1  Book  IV,  Chap.  XVII, 
Y 


322    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

exactly  to  fit  the  conditions  laid  down  in  Cesar's  text, 
may  be  an  excellent  illustration  of  that  text,  it  does  not 
follow  that  it  is  a  good  illustration  for  the  use  of  a  party 
of  men  proposing  to  make  a  bridge  over  the  Rhine, 
and  that  not  because  engineering  has  advanced  since 
Caesar's  tune,  but  because  the  whole  problem  of  the 
strength  of  materials  has  to  be  recast  according  to  the 
actual  dimensions  of  the  real  bridge.  Stresses  and 
strains  do  not  have  the  same  effect  upon  the  same  mate- 
rial under  different  conditions  of  dimension.  This  is 
why  practical  men  in  general,  and  engineers  in  particu- 
lar, use  models  for  certain  parts  of  their  work,  but  pre- 
fer to  test  their  results  on  the  true  scale  before  they  are 
willing  to  apply  them. 

In  the  case  of  class  work  our  principle  should  be  the 
same  as  the  engineer  finds  useful  in  his  actual  operations : 
begin  with  the  real  object,  and  end  with  the  real  object, 
but  between  the  two  use  the  model  as  freely  as  you  like. 
In  school  we  very  commonly  use  models  that  involve 
a  high  degree  of  abstraction.  In  the  teaching  of  botany 
we  may  have  a  greatly  enlarged  model  of  the  primrose 
made  of  papier  mdche.  The  form  may  be  a  perfect 
reproduction  of  that  of  the  real  flower;  the  colour  a  some- 
what less  accurate  reproduction.  But  there  the  resem- 
blance stops.  Abstraction  is  made  of  size,  flexibility, 
moisture,  texture,  scent.  The  sole  value  of  the  model  is 
that  its  size  enables  the  teacher  to  give  a  demonstration 
to  the  whole  class.  To  facilitate  this  the  model  is  made 
up  of  distinct  parts  which  can  be  separated  from  each 
other  so  that  the  teacher  can  make  a  formal  dissection 
of  the  model,  which  dissection  may  be  afterwards  imi- 
tated by  the  members  of  the  class  while  dealing  with 
the  real  specimens  with  which  they  are  then  provided. 


MATERIAL  ILLUSTRATIONS  323 

For,  wherever  possible,  the  teacher  should  follow  the 
example  of  the  engineer,  and  end  all  his  model  work 
by  a  reference  to  the  actual  object.  The  pupils  should 
begin  with  an  examination  of  a  real  primrose  actually 
growing  in  the  garden  or  in  a  pot.  Then  comes  the 
demonstration  on  the  magnified  model,  and  finally 
the  examination  by  each  pupil  of  the  cut  specimen 
supplied. 

The  same  sort  of  models  are  used  in  the  teaching 
of  biology.  The  cockchafer  is  selected  as  the  typical 
insect,  and  there  is  a  highly  complex  dissectible  model 
constructed  for  class  demonstrations.  But  a  still  higher 
degree  of  abstraction  is  reached  in  a  series  of  hollow 
models  of  some  forty  animals  produced  by  a  well-known 
maker  of  school  apparatus.  One  can  understand  the 
use  of  models  in  illustrating  the  outward  appearance 
of  such  creatures  as  the  elephant,  the  camel,  and  the 
bear;  but  when  it  comes  to  the  horse,  the  cow,  and  the 
dog  it  may  be  naturally  asked  wherein  consists  the  use- 
fulness of  a  set  of  models  of  creatures  that  may  be  con- 
veniently seen  in  real  life.  One  obvious  answer  is  that 
the  models  indicate  the  relative  sizes  of  the  different 
animals;  for  in  the  series  referred  to  the  creatures  are 
all  made  to  a  common  scale.  In  the  next  place,  the 
models  are  available  in  school,  and  enable  the  pupils  to 
make  certain  observations  that  may  be  tested  by  a 
later  examination  of  the  actual  animals  as  found  in  the 
open  air.  The  objection  that  the  models  are  mere 
shells  of  animals  is  hardly  of  much  consequence.  The 
child  sees  as  much  of  the  inside  of  the  model  cow  as  he 
sees  of  the  inside  of  the  cow  in  the  field.  Further, 
such  models  rouse  an  interest  in  familiar  animals  that 
the  animals  themselves  cannot  command.  Just  as  the 


324    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

cows  in  a  landscape  in  a  drawing-room  attract  much 
more  attention  than  they  ever  did  in  the  meadow,  so 
the  models  in  school  interest  the  children  more  than  do 
the  real  animals  —  always  taking  it  for  granted  that 
we  are  dealing  with  animals  that  have  exhausted  the 
charms  of  novelty.  A  papier  mdche  camel  has  little 
chance  of  surpassing  the  attractions  of  the  live  one. 
But  in  the  case  of  the  horse  it  is  different.  Most  of 
us  will  look  with  interest  at  a  model  of  something  that 
we  pay  no  attention  to  when  we  meet  it  in  real  life. 
Advertisers  have  not  been  slow  to  profit  by  this  interest 
in  models,  as  is  seen  by  the  many  tiny  samples  sent  out, 
in  which  the  characteristic  bottle  or  packet  that  con- 
tains the  commodity  is  exactly  reproduced,  but  on  a 
very  small  scale.  The  same  interest  is  appealed  to 
when  the  advertiser  sends  out  a  cart  bearing  a  mam- 
moth representation  of  the  bottle  or  packet. 

It  goes  without  saying  that  the  special  value  of  the 
model  lies  in  the  fact  that  it  gives  us  all  three  dimensions. 
It  is  therefore  assumed  that  it  is  necessarily  a  better 
form  of  illustration  than  anything  in  the  way  of  a  draw- 
ing, which,  after  all,  can  never  get  beyond  two  dimen- 
sions, with  a  suggestion  of  the  third.  The  model  may 
be  viewed  from  many  different  standpoints,  and  against 
different  backgrounds.  It  is  sometimes  said  that  a 
model  of  the  reconstructed  Parthenon  at  Athens  con- 
veys a  much  more  accurate  conception  of  what  it  was 
once  like  than  can  any  mere  plan  and  elevation  sketches. 
But  for  certain  purposes  a  picture  is  a  better  illustration 
than  a  model.  For  example,  a  picture  of  the  Parthe- 
non painted  by  a  sympathetic  artist,  with  the  model 
to  keep  him  right  in  detail,  and  his  own  trained  imagi- 
nation to  interpret  in  terms  of  colour  the  old  surround- 


MATERIAL  ILLUSTRATIONS  325 

ings,  will  probably  convey  a  better  impression  of  what 
was  the  real  state  of  things  in  old  Athens  than  does 
the  mere  dead  model.  This  is  perhaps  a  characteristic 
of  the  model,  that  it  confines  itself  to  the  bare  primary 
details.  The  artist's  lay  figure  does  all  that  is  expected 
of  it  when  it  keeps  him  straight  with  regard  to  the 
three  dimensions.  Within  these  limits  it  does  its  work 
admirably,  but  it  carries  with  it  no  suggestion  of  reality. 
There  is  always  something  unreal  in  a  complicated 
model  that  is  not  necessarily  present  in  a  picture. 
Take,  for  example,  those  elaborate  models  of  various 
cities  and  ports  that  have  been  exhibited  at  certain  of  the 
great  exhibitions  in  different  parts  of  the  world.  (A 
permanent  collection  of  this  kind  is  to  be  seen  in  the 
upper  regions  of  the  Louvre  in  Paris.)  The  observer 
has  thrust  upon  him  an  inevitable  feeling  of  triviality. 
The  models  have  all  the  appearance  of  toys.  They 
are  excellent  to  work  from.  They  give  us  a  general 
view  of  the  city  and  its  approaches  such  as  we  could  not 
get  from  any  available  point  of  view  in  the  district. 
We  can  in  a  few  minutes,  by  means  of  compasses  and 
scales,  get  any  desired  measurements.  But  we  cannot 
get  rid  of  the  feeling  of  unreality  and  childishness. 
So  in  dealing  with  the  accurate  models  of  great  build- 
ings of  which  the  Germans  are  so  fond.  These  models 
are  excellent  in  demonstrating  shapes  and  measure- 
ments, but  they  are  useless  in  reproducing  the  aesthetic 
effect  of  the  actual  buildings.  We  can  extract  no  en- 
thusiasm from  a  model  of  St.  Peter's  at  Rome.  The 
abstraction  of  size  has  destroyed  its  power  to  impress  us. 
Models  of  the  Gothic  Cathedrals  have  a  stronger  aes- 
thetic effect  upon  us  than  have  models  of  the  severer 
buildings  of  the  classical  times.  When  the  old  temples 


326    EXPOSITION   AND  ILLUSTRATION  IN  TEACHING 

have  lost  the  grandeur  that  their  spaciousness  gave  them, 
they  have  nothing  left.  The  Gothic  Cathedrals,  too,  lose 
their  grandeur,  but  in  its  place  there  comes  a  certain 
prettiness.  Awe  is  a  sentiment  that  cannot  be  repre- 
sented on  a  reduced  scale.  Models  can  reproduce  pro- 
portions, but  not  sentiments.  They  have  all  the  defects 
of  the  diagram  as  well  as  its  merits.  They  are  indeed 
nothing  more  than  three-dimensioned  diagrams. 

It  is  because  we  live  in  a  three-dimensioned  world 
that  the  model  deserves  a  place  among  our  illustrative 
apparatus.  Our  daily  experience  makes  it  impossible 
for  us  to  overlook  the  third  dimension ;  but  overf  amiliar- 
ity  with  two-dimensioned  illustrations  is  very  apt  to  lead 
to  an  unintelligent  way  of  regarding  certain  matters. 
The  globe,  for  example,  is  necessary  to  counteract  the 
impression  produced  by  the  "  World  in  Hemispheres  " 
as  it  is  presented  to  us  at  the  beginning  of  our  atlases. 
It  is  true  that  the  globe  in  its  turn  is  subject  to  abuse. 
In  his  usual  aggravating  way  Rousseau  makes  us  uncom- 
fortable by  calling  it  nothing  but  a  plaster  ball.  But 
the  teacher  does  not  want  it  to  be  anything  else.  So 
long  as  he  uses  it  as  an  illustration  he  is  proclaiming  that 
it  stands  for  something  that  it  is  not.  Its  merit  is  in 
its  shape,  not  in  its  material.  This  shape  prevents  the 
illustrator  from  taking  certain  liberties  that  he  allows 
himself  when  he  has  got  rid  of  the  third  dimension. 
He  wants,  for  example,  to  show  that  the  British  Isles  oc- 
cupy the  enviable  position  of  being  in  the  very  centre 
of  the  land  hemisphere.  Accordingly,  he  does  violence 
to  all  the  known  systems  of  map  projection  and  com- 
bines the  two  hemispheres  into  a  heart-shaped  whole. 
The  British  Isles  appear  in  their  true  projection  on  the 
middle  line  that  marks  the  junction  of  the  two  halves  of 


MATERIAL  ILLUSTRATIONS  327 

the  heart,  while  all  the  rest  of  the  world  wriggles  about 
in  greater  or  less  degrees  of  distortion.  The  proper 
way  to  illustrate  the  fact  of  the  central  position  of  the 
British  Isles  is  to  take  up  a  globe  and  turn  it  so  that  the 
pupil  is  looking  at  it  in  such  a  way  that  he  sees  the  great- 
est total  amount  of  land  that  it  is  possible  for  him  to 
include  in  one  view.  Once  the  model-world  is  placed  in 
this  position,  the  pupil  is  invited  to  look  for  the  British 
Isles.  As  a  matter  of  fact,  he  will  find  them  not  far 
from  the  centre  of  the  part  of  the  world  at  that  moment 
visible  on  the  globe. 

It  is  in  connection  with  the  seasons  and  the  rotation  of 
the  earth  that  the  use  of  a  tangible  ball  is  of  importance 
as  an  illustration.  No  doubt  in  teaching  such  matters 
as  longitude  and  latitude  it  is  necessary  to  have  a  prop- 
erly constructed  globe,  with  all  the  conventional  signs 
properly  filled  in.  The  practical  teacher  is  very  often 
tempted  to  regard  this  orthodox  globe,  with  its  axis 
fixed  at  the  proper  angle  of  23^°,  as  itself  the  illus- 
trandum.  He  talks  about  "teaching  the  globes," 
whereas  what  he  wants  to  say  is  that  he  teaches  certain 
relations  by  means  of  the  globe.  When  the  earth's 
relation  to  the  sun  and  to  the  other  planets  is  to  be 
illustrated,  it  is  better  to  have  a  less  formal  ball  to  deal 
with.  In  practice  it  is  found  that  a  ball  of  worsted 
with  a  knitting  needle  thrust  through  the  middle  to 
represent  the  axis  is  about  as  useful  a  form  of  globe  as 
can  be  found.  Each  pupil  should  be  supplied  with 
such  a  ball,  and  should  be  called  upon  to  manipulate  it 
as  the  teacher  describes  certain  of  the  phenomena  of 
the  earth's  rotation  and  revolution.  At  the  testing 
stage  it  is  well  that  only  one  pupil  at  a  time  should 
manipulate  a  ball,  as,  if  the  class  works  collectively, 


328    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

there  will  be  little  else  than  imitation  in  the  case  of  a 
great  many  of  the  boys. 

A  very  interesting  comparison  of  the  relative  values 
of  the  two-dimensioned  and  the  three-dimensioned 
illustration  may  be  had  from  comparing  the  results  of 
teaching  from  a  diagram  and  teaching  from  the  use  of 
the  ball.  The  familiar  diagram  of  the  sun  at  one  of  the 
foci  of  an  ellipse  with  the  earth  in  the  four  positions 
on  the  circumference  corresponding  to  the  four  seasons 
may  be  fully  understood  by  the  class.  That  is,  the 
pupils  may  be  able  to  say  honestly  that  they  understand 
the  diagram  and  are  able  to  answer  questions  on  it.  Now 
arrange  for  an  experiment.  On  a  table  on  an  open 
space  on  the  floor  place  a  candle  or  anything  else  that 
will  represent  the  sun,  and  then  call  out  one  of  the 
pupils  and  ask  him  to  carry  his  ball  of  worsted  round  the 
supposed  sun,  in  such  a  way  as  to  represent  the  revolu- 
tion of  the  earth,  and  thus  demonstrate  the  cause  of 
the  seasons.  In  a  large  percentage  of  cases  in  which 
this  experiment  has  been  made,  the  pupil  moved  round 
the  sun,  keeping  the  axis  jealously  fixed  at  what  he 
believed  to  be  23|°  from  the  vertical,  but  point- 
ing at  the  sun  all  the  time.  This  occurs  even  when 
stress  has  been  laid  by  the  teacher  on  the  fact  that  the 
earth's  axis  is  always  "parallel  to  itself."  The  fixed  angle 
of  23|°  satisfies  the  mind's  requirement  in  this  respect, 
and  nothing  short  of  the  Confrontation  implied  in  the 
permanent  winter  of  the  side  remote  from  the  sun  in 
the  actual  experiment  will  rouse  the  pupil  to  the  neces- 
sary dissatisfaction  with  his  view  as  gathered  from  the 
plane  diagram. 

An  orrery  supplies  a  striking  example  of  ineffective- 
ness in  illustration.  The  motions  of  the  planets  and 


MATERIAL  ILLUSTRATIONS  329 

their  satellites  can  be  reproduced  in  a  very  accurate 
way,  but  the  mental  effect  of  the  whole  is  discouraging. 
The  distance  effect  is  as  much  lacking  here  as  in  the 
case  of  models  of  huge  buildings.  Sir  John  Herschel 
speaks  very  strongly  of  the  futility  of  giving  an  idea  of 
the  sizes  and  distances  of  the  planets  by  this  means, 
and  sets  forth  a  scheme  of  his  own  to  convey  the  desired 
information :  — 

"Choose  any  well-levelled  field  or  bowling-green.  On  it  place 
a  globe  two  feet  in  diameter ;  this  will  represent  the  sun ;  Mercury 
will  be  represented  by  a  grain  of  mustard  seed,  on  the  circumference 
of  a  circle  164  feet  in  diameter  for  its  orbit ;  Venus  a  pea,  on  a  circle 
284  feet  in  diameter ;  the  Earth  also  a  pea,  on  a  circle  of  430  feet ; 
Mars  a  rather  large  pin's  head,  on  a  circle  of  654  feet ;  Juno,  Ceres, 
Vesta,  and  Pallas  grains  of  sand  in  orbits  of  from  1000  to  1200  feet ; 
Jupiter  a  moderate-sized  orange,  in  a  circle  nearly  half  a  mile  across ; 
Saturn  a  small  orange,  on  a  circle  of  four-fifths  of  a  mile ;  Uranus  a 
full-sized  cherry,  or  small  plum,  upon  the  circumference  of  a  circle 
more  than  a  mile  and  a  half ;  and  Neptune  a  good-sized  plum  on  a 
circle  about  two  miles  and  a  half  in  diameter.  As  to  getting  correct 
notions  on  this  subject  by  drawing  circles  on  paper,  or,  still  worse, 
from  those  very  childish  toys  called  orreries,  it  is  out  of  the  ques- 
tion." » 

This  illustration  fails  in  many  directions.  To  begin 
with,  there  is  a  lack  of  a  definite  standard  of  size. 
What  is  the  standard  size  of  a  pea,  a  cherry,  a  plum,  an 
orange  ?  Who  is  to  determine  how  big  a  large  pin's 
head  is  ?  Further,  whatever  the  real  size  of  a  pea,  the 
effect  that  the  illustration  produces  on  the  mind  of  the 
ordinary  reader  is  that  Venus  is  larger  than  it  really  is 
in  proportion  to  the  earth.  If  it  is  said  that  all  that  is 
wanted  is  to  convey  a  general  impression,  the  answer 
is  that  the  illustration  invites  comparisons,  and  suggests 

1  Outlines  of  Astronomy  (1849),  p.  323. 


330    EXPOSITION   AND  ILLUSTRATION   IN  TEACHING 

by  its  discrimination  among  the  various  qualifying 
adjectives  that  the  comparisons  are  accurate.  Again, 
the  distances  should  be  kept  to  the  same  standard: 
they  ought  all  to  be  expressed  in  feet.  These  criticisms 
are  not  the  outcome  of  arm-chair  reflection.  They 
express  the  complaints  of  many  classes  of  students 
(ages  ranging  from  eighteen  to  twenty-one)  who  have 
been  offered  instruction  through  this  illustration. 

The  truth  is  that  what  are  called  real  illustrations, 
those  that  deal  with  actual  objects,  have  the  defects  of 
their  quality,  and  fail  because  of  the  very  virtue  on  which 
real  illustration  prides  itself  —  reality.  Three-dimen- 
sioned illustrations  sadly  hamper  the  freedom  of  the 
pupil's  imagination.  If  we  are  to  picture  certain  grains 
of  sand  in  a  preposterous  bowling-green  two  and  a  half 
miles  wide,  we  find  that,  so  far  from  being  helped  by  our 
illustration,  we  are  really  hindered  in  our  efforts  to 
figure  out  the  sizes  and  distances  of  the  planets.  Her- 
schel's  illustration  certainly  aids  us  in  respect  of  the 
concept  of  distance,  and  gets  rid  of  the  toy  effect 
of  the  orrery;  but  in  so  far  as  it  substitutes  peas  and 
cherries  for  the  spheres  of  the  orrery,  it  introduces  limit- 
ing elements.  After  all,  a  diagram  leaves  the  mind 
freer  than  do  these  concrete  comparisons. 

Sir  John  Herschel's  illustration  has  been  largely  used 
by  teachers,  and  it  is  interesting,  to  note  the  changes 
they  have  made.  It  is  generally  used  in  schools  in  tabu- 
lar form  rather  than  as  a  description.  Venus  is  rep- 
resented by  "a  pea,"  but  the  earth  by  "a  larger  pea"  — 
so  strong  is  the  teacher's  love  of  accuracy  and  the  pupils' 
of  fair  play.  The  only  other  important  change  is  that 
many  teachers  prefer  to  cut  down  the  distances  by  one- 
half,  taking  the  radius  in  preference  to  the  diameter. 


MATERIAL  ILLUSTRATIONS  331 

Another  debatable  use  of  the  solid  as  illustration  is 
to  be  found  in  the  glyptic  formulae  of  Hofmann.  Not 
content  with  the  elaborate  patterns  of  the  graphic 
formulae  that  were  used  to  represent  such  complicated 
chemical  combinations  as  Dicobaltic  tetrammon-hexa- 
ammonic  hexachloride  (called  purpureo-cobalt  chloride, 
for  short),  Hofmann  launched  out  into  the  third  dimen- 
sion, and  invented  a  system  of  spheres  of  about  the  size 
of  billiard  balls l  of  various  colours,  each  having  one  or 
more  little  tubes  projecting  from  its  surface,  accord- 
ing as  it  was  intended  to  represent  a  monad,  a  dyad, 
or  an  atom  of  some  higher  valency.  By  means  of  con- 
necting rods  of  various  curvature,  Hofmann  was  able  to 
build  up  symmetrical  combinations  to  indicate  how  the 
elements  united  with  each  other  and  formed  more  or 
less  permanent  wholes.  It  is  doubtful  whether  any- 
thing was  gamed  by  all  this  elaboration,  for  the 
models  did  not  even  pretend  to  reproduce  a  state  of 
affairs  that  actually  existed.  If  Sir  John  Herschel 
fails  in  making  us  realise  the  solar  system,  it  is  because 
we  cannot  properly  represent  what  actually  exists. 
In  the  case  of  the  chemical  formulae,  the  teacher  has  to 
warn  his  pupils  against  imagining  that  what  he  sees 
in  the  model  represents  what  actually  takes  place  in 
chemical  process.  Dr.  Edward  Frankland,  of  the 
Royal  College  of  Chemistry,  London,  himself  an  excel- 
lent teacher,  made  extensive  use  of  both  glyptic  and 
graphic  formulae.  He  tells  us  in  the  Preface  to  his 
well-known  compendium : 2  — 

1  Later,  the  tetrahedral  form  was  introduced  to  enable  the  teacher 
to  give  demonstrations  of  combining  molecules  by  means  of  common 
elements. 

2  Lecture  Notes  for  Chemical  Students,  1866. 


332    EXPOSITION   AND   ILLUSTRATION   IN   TEACHING 

"  I  am  aware  that  graphic  and  glyptic  formulae  may  be  objected 
to  on  the  ground  that  students,  even  when  specially  warned  against 
such  an  interpretation,  will  be  liable  to  regard  them  as  representa- 
tions of  the  actual  physical  position  of  the  atoms  of  compounds. 
In  practice  I  have  not  found  this  evil  to  arise ;  and  even  if  it  did 
occasionally  occur,  I  should  deprecate  it  less l  than  ignorance  of  all 
notions  of  atomic  constitution." 

But  surely  the  concluding  sentence  is  somewhat 
strong.  Are  we  shut  up  to  the  alternative  of  glyptic 
formulae  or  "  ignorance  of  all  notions  of  atomic  consti- 
tution" ?  The  fact  is  that  there  are  types  of  mind  that 
find  the  glyptic  formulae  repellent,  and  others  that  revel 
in  them  with  such  delight  as  to  lead  to  danger  of  con- 
founding the  illustration  with  the  illustrandum.  The 
other  day  a  student  of  the  second  type  brought  forward 
a  scheme  for  making  "a  model  of  the  mind"  on  glyptic 
principles.  Each  idea  was  to  be  represented  by  a  ball, 
and  the  apperception  masses  were  to  be  built  up  sepa- 
rately, and  then  combined  with  each  other  by  uniting 
the  different  masses  by  means  of  common  elements. 
Reflection  for  a  few  minutes  shows  how  unworkable  the 
scheme  is,  and  yet  it  has  great  possibilities  in  the  way 
of  illustration.  One  of  its  main  advantages  would  be 
that  it  would  convince  the  students  that  an  atomic 
theory  of  ideas  is  only  an  illustration  of  a  system  that 
cannot  be  fully  explained  on  this  basis. 

When  material  illustrations  are  used  in  connection 
with  solid  geometry,  they  have  to  fulfil  the  very  function 
that  Dr.  Frankland  warned  his  students  against.  They 
must  be  "representations  of  the  actual  physical  posi- 
tion" of  the  elements  of  the  illustrandum.  There  can 

1  Yet  it  was  with  regard  to  one  of  the  plates  of  graphic  formulae 
in  Dr.  Frankland's  book  that  the  Oxford  don  remarked,  "  Ah,  I  sup- 
pose that  is  how  the  gases  look  under  the  microscope." 


MATERIAL   ILLUSTRATIONS  333 

be  no  question  of  the  value  of  cardboard  models  in 
illustrating  the  exasperating  little  diagrams  that  adorn 
the  eleventh  book  of  Euclid,  even  though  the  severe 
mathematician  looks  askance  at  any  attempt  to  rep- 
resent the  realities  of  which  he  makes  abstraction. 
In  projection,  sections,  development,  and  penetration 
the  use  of  standard  models  is  of  the  greatest  value. 
Often  all  that  is  wanted  is  a  glance  at  the  actual  model. 
It  is  different  with  some  of  the  elaborate  apparatus  de- 
vised to  make  dull  students  understand  the  projection 
of  points  and  lines  on  the  two  coordinate  planes.  After 
taking  many  classes  through  a  course  in  descriptive 
geometry,  and  using  with  them  all  manner  of  appara- 
tus, I  am  convinced  that,  in  teaching  the  elements  of  the 
subject,  all  the  elaborate  arrangements  of  beads  and 
threads  and  pins  are  worse  than  useless.  If  the  candi- 
date cannot  understand  the  dots  and  lines  above  and 
below  the  line  of  intersection  in  a  given  diagram,  he  is 
not  at  all  likely  to  understand  the  aggravating  complica- 
tions introduced  by  way  of  illustration.  This  is  one  of 
the  cases  in  which  the  illustrandum  is  clearer  than  the 
illustration.  An  arrangement  in  cardboard  or  wood  by 
which  the  two  coordinate  planes  can  be  represented  as 
cutting  each  other,  and  thus  showing  the  four  dihedral 
angles  and  the  line  of  intersection  (almost  universally 
named  X  F)  is  a  simple  piece  of  apparatus  that  should 
always  be  available.  It  is  usually  made  so  that  the  two 
coordinate  planes  may  be  made  to  rotate  on  XY  so  as 
to  (practically)  coincide,  and  thus  illustrate  the  relation 
of  the  various  dihedral  angles  to  the  plane  of  the  paper 
on  which  the  pupil's  drawing  is  to  be  made.  Such  a  bit 
of  apparatus  is  extremely  simple,  and  leaves  the  pupil's 
imagination  quite  free  with  regard  to  individual  prob- 


334    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

lems,  while  rigidly  restricting  it  as  to  the  conditions  of 
all  problems. 

Generally  speaking,  there  is  a  tendency  in  all  material 
illustrations  to  become  too  elaborate,  and  the  teacher  is 
apt  to  think  that  their  value  is  in  proportion  to  the 
amount  of  time  he  spends  in  their  preparation.  In 
actual  teaching  their  value  is  often  in  inverse  ratio. 
It  is  different  in  the  case  in  which  the  pupils  themselves 
take  a  part  in  preparing  the  apparatus.  When  this 
occurs,  they  acquire  that  familiarity  with  the  subject 
that  in  the  other  case  is  confined  to  the  teacher. 

The  ideal  use  of  teaching-models  is  to  have  them 
made  by  the  pupils,  not  merely  as  teaching-illustra- 
tions but  as  a  substantive  part  of  their  intellectual  work. 
It  is  not  a  case  of  making  things,  but  of  thinking  thoughts 
and  expressing  them  in  a  material  form.  My  colleague, 
Dr.  T.  Percy  Nunn,  has  contrived  to  get  several  classes 
of  quite  young  pupils  to  make  drawings  and  models 
embodying  their  own  observations  of  the  sun  and  the 
moon,  and  has  obtained  astonishing  results  in  the  way 
of  clear  thinking  on  matters  that  greatly  puzzle  most 
adults.  Boys  of  twelve,  starting  from  the  daily  measure- 
ment of  the  sun's  shadow  at  noon,  have  themselves 
worked  out  all  the  calculations  necessary  to  develop  the 
curve  of  the  sun's  apparent  path  through  the  heavens, 
and  ended  by  making  a  cardboard  model  of  this  path 
in  such  a  way  as  to  make  clear  the  relation  between 
the  apparent  path  of  the  sun  and  the  real  path  of  the 
earth.  These  boys  talk  on  such  matters  now  with  an 
ease  that  disconcerts  the  ordinary  educated  man,  who 
has  always  to  pause  and  reflect  before  he  ventures  to 
make  any  statement  that  correlates  the  real  with  the 
apparent  in  the  movements  of  the  heavenly  bodies. 


MATERIAL  ILLUSTRATIONS  335 

Dr.  Nunn  himself  writes:  "I  always  regard  my  models 
as  being  devices  to  aid  the  boy  in  'colligating'  his  own 
observations.  They  differ  from  the  usual  models  in 
not  aiming  at  dispensing  with  first-hand  observations. 
That  is,  I  think,  why  they  are  effective.  The  boy 
thinks  of  the  facts  by  the  aid  of  the  symbols." 


CHAPTER  XIV 

THE  PICTURE  AS  ILLUSTRATION 

FROM  one  point  of  view  a  picture  is  necessarily  more 
abstract  than  a  model.  One  aspect  of  reality  is  seized 
upon  and  elaborated.  Even  in  the  case  of  the  mere  re- 
production of  reality  in  a  photograph  there  is  abstrac- 
tion. We  are  limited  to  one  point  of  view  and  to  the 
corresponding  background.  The  model  may  be  viewed 
from  many  standpoints,  and  from  each  standpoint  there 
is  a  different  background.  All  the  laws  of  linear  per- 
spective enrich  the  possibilities  of  models  as  illustrations. 
When  we  consider  aerial  perspective  and  the  laws  of 
colour,  we  find  still  further  need  for  abstraction  forced 
upon  the  picture  as  a  means  of  illustration.  The 
painter  must  select  the  particular  set  of  colours  that  mark 
the  moment  chosen  for  the  painting.  The  fact  that  the 
colours  of  an  object  or  a  scene  change  from  hour  to  hour, 
almost  from  moment  to  moment,  has  always  been  known, 
but  has  of  late  years  been  more  clearly  recognised. 
The  school  of  Impressionist  painters  have  done  valu- 
able work  in  bringing  home  to  us  this  important  fact. 
They  claim  that  it  is  the  artist's  business  to  paint  light 
as  represented  by  colour.  They  ought  to  be  called 
Chromatists  rather  than  Impressionists.  One  cannot 
look  at  Claude  Monet's  series  of  hay-ricks  or  cathedrals 
without  realising  that  one  picture  can  represent  only  one 
out  of  many  aspects  of  the  same  object  in  respect  of 

336 


THE  PICTURE  AS  ILLUSTRATION  337 

colour,  just  as  it  can  represent  only  one  aspect  with  re- 
gard to  linear  perspective.  This  painter's  methods  in 
his  careful  studies  of  light  and  colour  have  been  thus 
described :  — 

"He  is  said  to  take  with  him  in  a  carriage  at  sunrise  some 
twenty  canvases  which  he  changes  from  hour  to  hour,  taking  them 
up  again  the  next  day.  He  notes,  for  example,  from  nine  to  ten 
o'clock  the  most  subtle  effects  of  sunlight  upon  a  hay- rick ;  at  ten 
o'clock  he  passes  on  to  another  canvas  and  recommences  the  study 
until  eleven  o'clock.  Thus  he  follows  step  by  step  the  modifica- 
tions of  the  atmosphere  until  nightfall,  and  finishes  simultaneously 
the  whole  series.  He  has  painted  a  hay-stack  in  a  field  twenty  times 
over,  and  the  twenty  hay-stacks  are  all  different.  He  exhibits 
them  together,  and  one  can  follow,  led  by  the  magic  of  his  brush, 
the  history  of  light  playing  upon  one  and  the  same  object."  l 

When  we  examine  these  early  morning  hay-ricks,  late 
morning  hay-ricks,  noontide  hay-ricks,  afternoon  hay- 
ricks, and  evening  hay-ricks,  we  find  that  each  has  its 
individuality,  and  yet  there  is  only  one  "real  hay-rick." 
If  there  be  this  great  range  in  the  case  of  such  an  emi- 
nently good  sitter  as  a  hay-rick,  what  must  be  said  of 
the  portrait  painter's  work  ?  What  help  can  we  expect 
from  a  portrait  in  forming  an  idea  of  even  what  a  man's 
outward  appearance  is  like,  to  say  nothing  of  what  his 
character  is?  Some  historical  portraits  are  done  in 
triplicate,  the  group  including  a  front  view  and  the 
two  profiles.  This  gives  us  a  certain  amount  of  help, 
but  for  a  complete  illustration  of  the  appearance  of  an 
historical  character  we  would  require  a  gallery  of  por- 
traits. Were  it  not  that  Velasquez  was  a  court  painter, 
we  might  look  to  his  many  pictures  of  Philip  IV  as  at 

1  Camille  Mauclair :  The  French  Impressionists,  English  translation, 
p.  130. 


338    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

least  approximate  material  for  forming  an  idea  of  how 
that  monarch  really  looked. 

In  view  of  all  this  limitation  in  the  case  of  persons 
who  really  existed,  what  are  we  to  say  when  we  come 
to  deal  with  matters  in  which  there  is  no  longer  any 
standard  in  existence  ?  If  we  are  so  doubtful  about  the 
mere  face  of  an  important  character  hi  an  historical 
scene,  we  can  realise  to  some  extent  how  helpless  we  are 
in  the  hands  of  the  historical  painter.  There  are  indeed 
as  many  Fields  of  the  Cloth  of  Gold  as  there  are  painters 
who  have  ventured  to  reproduce  the  scene.  Naturally 
this  raises  the  question  of  the  value  of  pictures  in  text- 
books of  history.  Some  teachers  object  to  any  picture 
that  does  not  confine  itself  to  the  mere  details  of  dress, 
architecture,  and  general  archa3ological  matters  of  which 
we  have  certain  knowledge.  From  this  point  of  view 
historical  illustration  is  a  sort  of  antiquated  fashion- 
plate.  The  ideal  illustrations  would  have  to  be  culled 
from  the  learned  German  tomes  that  contain  reproduc- 
tions of  the  fluctuating  fashions  throughout  the  cen- 
turies. 

Such  teachers  maintain  that  all  pictures  describing 
an  actual  incident  must  of  necessity  be  wrong.  The 
one  thing  that  may  safely  be  asserted  about  the  incident 
is  that,  however  it  happened,  it  did  not  happen  in  just 
the  way  the  painter  has  represented.  Mathematical 
laws  are  invoked  to  prove  the  infinitely  remote  chance 
of  all  the  combinations  coming  right  in  a  given  repre- 
sentation of  the  incident. 

If  you  care  to  go  to  the  Ashmolean  Museum  at  Ox- 
ford, you  will  find  under  a  glass  case  certain  pieces  of 
old  iron  that  are  labelled  as  being  the  identical  lantern 
used  by  Guy  Fawkes  on  a  certain  fateful  fifth  of  Novem- 


THE  PICTURE  AS  ILLUSTRATION  339 

her.  It  does  not  appear  that  there  is  any  question  about 
the  genuineness  of  the  debris,  and  visitors  are  sometimes 
able  to  get  up  quite  a  pleasant  degree  of  excitement  at 
the  sight  of  the  scrap-iron.  The  fashion-plate  teachers 
regard  the  remains  with  favour,  and  would  willingly 
provide  all  English  schools  with  at  least  a  photograph  of 
them  in  the  unavoidable  absence  of  the  inspiring  origi- 
nals. To  these  teachers  a  spirited  picture  of  the  arrest 
of  the  traitor  is  regarded  as  dangerously  misleading, 
because  it  cannot  possibly  be  "true." 

"Do  these  little  people,"  we  may  ask,  with  a  distinguished 
American  novelist,  "know  that  Scott's  archaeology  was  about  one 
thousand  years  'out'  in  Ivanhoe,  and  that  to  make  a  parallel  we 
must  conceive  of  a  writer  describing  Richelieu,  say,  in  small 
clothes  and  a  top  hat  ?  But  is  it  not  Richelieu  we  want,  and  Ivan- 
hoe,  not  their  clothes,  their  armour  ?  "  l 

All  the  same,  while  a  protest  is  necessary  against  the 
excessive  attention  given  to  archaeological  details,  there 
is  nothing  to  be  gained  by  deliberately  neglecting  them. 
//  Scott  is  one  thousand  years  wrong  in  his  archaeology, 
it  is  something  to  be  condoned,  not  admired.  Veronese's 
picture  of  the  "Marriage  at  Cana"  is  perhaps  none  the 
less  a  masterpiece,  though  he  has  put  the  people  into  the 
clothes  of  his  contemporaries;  but  the  work  is  not  im- 
proved by  the  anachronism.  As  teachers  we  must  be  as 
accurate  as  we  can  without  becoming  pedantic. 

The  points  to  be  determined  in  connection  with  a 
picture  of  an  historical  scene  as  illustration  are  mainly 
two:  the  one  negative,  the  other  positive.  First,  the 
picture  must  not  contain  anything  that  contradicts 
historical  evidence;  it  must  be  consistent  with  all  that 
we  know  of  the  period.  Secondly,  it  ought  to  throw 

1  Frank  Norris :  The  Responsibilities  of  the  Novelist,  1903,  p.  17. 


340    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

some  light  on  the  scene  depicted;  it  ought  to  embody 
an  idea. 

It  is  obvious  that  a  picture  may  fulfil  both  these 
conditions,  and  at  the  same  time  do  a  great  deal  to 
teach  the  details  of  the  dress,  architecture,  and  mode 
of  living  of  the  time.  The  danger  is  that  these  details 
may  become  too  prominent,  and  the  picture  acquire 
that  purposeless  air  that  marks  the  fashion-plate.  A 
novel  with  a  purpose  is  usually  a  poor  novel,  because  it 
was  not  the  writer's  main  purpose  to  make  a  good  novel. 
So  the  fashion-plate  picture  fails  because  its  purpose 
is  to  be  a  good  fashion-plate,  and  not  to  be  a  good 
picture. 

It  has  to  be  remembered  that  every  picture,  historical 
or  other,  however  well  executed,  limits  the  mind  of  the 
spectator  in  dealing  with  the  scene  depicted.  Once  a 
set  of  elements  have  been  combined  in  a  definite  way,  the 
mind  finds  it  difficult  to  break  up  the  connection  and 
recombine  them.  Young  clergymen  of  great  ability 
and  originality  have  complained  that  they  had  to  give 
up  reading  the  published  sermons  of  the  great  English 
preacher,  Robertson,  of  Brighton,  for  the  reason  that 
once  they  had  read  one  of  these  sermons,  the  text  re- 
mained ever  after  a  forbidden  one  for  them,  since  it  was 
impossible  to  preach  upon  it  without  seeming  to 
have  plagiarised.  The  treatment  of  the  subject  in  the 
printed  sermon  seemed  to  them  so  thorough  and 
altogether  so  satisfactory,  that  there  appeared  to  be  no 
other  way  in  which  it  could  be  properly  dealt  with. 

The  same  difficulty  is  experienced  by  anyone  who 
wishes  to  make  a  new  illustration  of  some  principle  that 
is  stated  and  particularly  well  illustrated  in  a  text-book. 
The  combination  of  elements  is  so  well  made  in  the 


THE  PICTURE  AS  ILLUSTRATION  341 

original  illustration  that  the  reader  finds  his  way  blocked. 
He  may  break  up  the  illustration  into  its  constituent 
ideas,  but  these  show  a  strong  tendency  to  recombine  on 
their  old  lines.  While  this  is  true  of  all  sorts  of  combi- 
nations, it  is  particularly  true  of  those  that  have  been 
formed  in  spatial  relations.  A  description  of  a  certain 
incident  may  be  given,  and  the  hearer  may  make  a 
more  or  less  vivid  mental  picture  of  the  occurrence  ; 
still,  as  a  rule,  this  picture  can  be  easily  replaced  by 
another.  But  if  the  scene  has  been  expressed  hi  terms 
of  space  and  colour  in  an  external  picture,  it  is  very  diffi- 
cult indeed  to  make  a  mental  reconstruction.  The  less 
exact  the  verbal  description  the  more  dangerous  is  the 
external  picture  as  a  determining  force,  for  the  more 
is  left  to  the  draughtsman.  Poetry,  for  example,  is  sel- 
dom well  illustrated.  For  this  there  are  two  reasons. 
First,  it  requires  a  poet  to  illustrate  a  poet.  So  far 
as  the  readers  of  a  poet  are  able  to  appreciate  his 
writings,  so  far  are  they  also  poets,  though  they  play  a 
more  passive  part  than  that  of  the  poet  who  writes. 
Apart  from  power  of  execution,  the  minimum  demand 
from  an  artist  who  proposes  to  illustrate  poetry  is  that 
he  should  be  himself  at  least  a  passive  poet.  The 
second  reason  is  that  many  of  the  most  charming  things 
in  a  poem  are  of  such  a  nature  that  they  cannot  be 
illustrated.  Their  merit  lies  in  their  elusiveness;  a 
certain  vagueness  is  of  their  very  nature.  To  make 
a  picture  of  Satan's  massive  bulk  as  he  "lay  floating 
many  a  rood"  is  to  reduce  poetry  to  a  more  or  less 
exact  science.  Whether  we  will  or  no,  a  picture  lends 
itself  to  drawing  to  scale. 

Minds  of  fine  calibre  usually  object  to  illustrations 
in  both  poetry  and  fiction.     The  artist  interferes  with 


342    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

their  freedom.  The  influence  of  the  fait  accompli  is 
powerful  in  all  departments  of  life,  but  nowhere  is  it 
more  powerful  than  here.  After  seeing  a  picture  of  a 
character  hi  a  novel,  it  is  very  difficult  indeed  to  con- 
ceive of  that  character  under  a  different  face.  Strongly 
imaginative  visuals  have  usually  invented  for  them- 
selves a  very  clearly  defined  picture  of  each  of  the 
characters  of  a  story,  and  of  characters  in  history  whose 
faces  have  not  been  handed  down  to  us.  Such  persons 
resent  any  picture  that  is  not  theirs.  They  say  that 
this  picture  is  not  like  the  character,  that  is,  is  not  like 
the  picture  they  have  formed  in  their  minds. 

But,  on  the  other  hand,  there  are  many  who  are  unable 
to  form  a  mental  picture  corresponding  to  a  descrip- 
tion. These  welcome  illustrations,  and  all  they  demand, 
is  that  the  illustration  shall  correspond  to  the  facts 
contained  in  the  text.  This  very  simple  demand  is  far 
less  frequently  complied  with  than  one  would  expect. 
Authors  have  a  standing  grievance  against  artists  for 
blundering  hi  their  representations  of  the  matters  dealt 
with  in  the  text.  The  author  makes  the  prisoner  gaze 
gloomily  at  the  four  tiny  squares  of  sunlight  that  the 
prison  window  allows  to  fall  upon  the  opposite  wall, 
and  the  artist  represents  nine  tiny  squares.  The  au- 
thor complains  that  the  artist  has  not  read  the  book 
with  sufficient  care.  On  the  other  hand,  the  artist 
often  complains  of  the  carelessness  of  the  author.  An 
artist  friend  of  mine  had  the  satisfaction  lately  of  writ- 
ing to  an  author  that  if  a  certain  character  were  to 
be  depicted  as  doing  what  the  author  said  he  did,  it 
would  be  necessary  to  draw  the  character  with  an  arm 
twenty  feet  long.  Indeed,  it  is  mainly  in  connection 
with  illustrations  that  discrepancies  between  different 


THE  PICTURE  AS  ILLUSTRATION  343 

parts  of  the  text  are  exposed.  Of  the  two  the  author 
has  the  safer  position.  He  may,  and  frequently  does, 
make  a  slip  in  his  topography  without  anyone  being  a 
bit  the  wiser.  A  careful  examination  of  the  work  of 
almost  any  popular  writer  of  fiction  will  show  up  some 
inconsistencies  that  have  never  been  found  out  by  the 
public,  because  the  different  parts  are  not  confronted 
with  each  other.  This  confrontation  is  frequently 
forced  on  by  the  artist,  whose  work  naturally  gives  itself 
over  to  criticism  of  this  kind. 

An  interesting  parallel  may  be  drawn  between  the 
concept  and  the  image,  on  the  one  hand,  and  the 
author-picture  and  the  artist-picture,  on  the  other. 
As  the  concept  has  the  power  of  crystallising  out  into  a 
definite  image,  so  the  author-conception  of  the  group- 
ing of  elements  may  be  crystallised  out  into  the  picture 
of  the  artist. 

The  artist  stands  between  the  author  and  the 
reader.  By  means  of  words  ideas  pas's  from  the  author 
to  the  reader.  So  far  as  these  ideas  are  capable  of 
pictorial  representation,  they  may  be  very  vaguely  set 
forth  in  the  author's  mind,  and  as  vaguely  in  the  minds 
of  many  of  his  readers.  Some  of  the  readers  may  have 
a  much  clearer  and  even  more  accurate  picture  than  the 
author  himself.  So  long  as  there  is  no  flagrant  contra- 
diction between  the  author-picture  and  the  reader- 
picture,  the  two  may  exist  comfortably  side  by  side  with- 
out either  author  or  reader  being  aware  how  different 
the  two  pictures  are.  This  agreement  in  difference  is 
possible  only  because  there  is  no  objective  standard  to 
which  both  pictures  may  be  referred.  The  moment  the 
artist  comes  along,  his  picture  supplies  the  missing 
standard,  and  both  author  and  reader  are  able  to  com- 


344    EXPOSITION   AND   ILLUSTRATION   IN   TEACHING 

pare  their  picture  with  this  external  standard.  Very 
often  the  artist's  picture  corresponds  neither  to  the 
author's  picture  nor  to  any  of  the  pictures  formed  by 
the  readers.  Indeed,  it  would  be  very  wonderful  if  the 
artist's  picture  did  coincide  at  all  points  with  any  other 
picture.  On  the  other  hand,  in  the  case  of  a  careful 
and  skilful  artist,  there  will  probably  be  no  justifiable 
difference  between  the  author's  account  and  its  transla- 
tion into  terms  of  space.  Each  reader  will  probably 
say,  "Well,  it  is  not  just  what  I  thought  it  would  be, 
but  it  is  quite  in  keeping  with  what  the  book  tells  us, 
so  I  suppose  it's  all  right."  It  sometimes  happens, 
indeed,  that  a  reader  of  exceptional  experience  may  have 
a  truer  picture  than  either  the  author  or  the  artist, 
if  by  truth  we  mean  fidelity  to  things  as  they  really  are. 
An  author,  for  example,  lays  the  scene  of  his  story  in  a 
country  that  he  has  never  visited.  He  has  carefully  read 
up  his  subject,  and  has  acquired  quite  a  store  of  second- 
hand local  colour.  The  book  is  illustrated  by  an  artist 
who  also  has  never  visited  the  country,  and  the  illustra- 
tions are  quite  satisfactory  to  the  author,  who  has  no  ob- 
jective standard  by  which  to  test  them.  On  the  other 
hand,  a  reader  who  knows  the  country  in  question  might 
read  the  unillustrated  book  with  pleasure  and  under- 
standing and  never  suspect  that  its  author  had  no  first- 
hand knowledge  of  the  country,  for  this  reader  would 
interpret  all  that  was  said  in  terms  of  his  own  experi- 
ence,1 and  would  form  for  himself  correct  pictures  with- 

1  An  excellent  illustration  of  what  goes  on  unconsciously  in  the 
mind  of  such  a  reader  is  to  be  found  in  the  twenty-ninth  chapter  of 
Ivanhoe,  where  the  wounded  knight  consciously  and  deliberately  inter- 
prets what  Rebecca  tells  him  about  the  doings  of  the  besiegers  of 
Torquilstone  Castle. 


THE  PICTURE  AS  ILLUSTRATION  345 

out  suspecting  that  they  did  not  correspond  to  what  had 
been  in  the  author's  mind.  Naturally,  if  the  author 
goes  into  detailed  descriptions,  he  is  almost  sure  to 
betray  himself  to  the  reader  who  really  knows,  but  he 
has  at  least  a  chance  of  getting  off  undetected,  and  I 
have  known  several  cases  in  which  such  an  author  has 
been  quite  successful.  But  so  soon  as  an  illustrated 
edition  falls  into  the  hands  of  the  specially  well-informed 
reader,  discrepancies  are  at  once  detected. 

It  is  much  easier  to  hide  one's  ignorance  in  writing 
than  in  drawing.  No  doubt  if  a  manuscript  by  an 
author  depending  upon  second-hand  knowledge  is 
submitted  to  minute  analysis  by  a  person  well  versed  at 
first  hand  in  the  matter  described,  it  is  almost  impossible 
for  it  to  stand  the  test.  But  the  artist  is  in  a  much 
worse  case.  He  plays  with  his  cards  on  the  table.  He 
has  a  certain  space  that  he  must  fill  somehow  or  other. 
No  doubt  he  is  able  to  arrange  matters  so  as  to  hide  a 
certain  amount  of  his  ignorance.  He  may  so  place  his 
figures  that  certain  portions  of  their  attire  or  accoutre- 
ments are  not  seen ;  he  may  foreshorten  certain  lengths 
of  which  he  is  not  sure,  and  make  the  laws  of  perspective 
responsible  for  any  apparent  discrepancy;  above  all, 
he  may  vaguely  suggest  certain  possibilities,  and  leave 
the  observer  to  fill  in  details  at  his  own  responsibility. 
This  last  method,  transferred  to  the  realm  of  letters,  is 
that  adopted  by  the  ordinary  author.  In  any  case  the 
worker  in  words  is  not  called  upon  to  describe  any- 
thing he  wishes  not  to  describe.  He  is  at  liberty  to 
select  for  description  whatever  pleases  him.  The 
artist,  on  the  other  hand,  must  meet  his  difficulties.  He 
cannot  merely  omit  them;  and  when  he  seeks  to  evade 
them,  he  has  to  do  so  in  a  way  that  is  easily  detected. 


346    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

In  a  certain  sense  the  artist  may  be  said  to  be  called 
upon  to  do  the  necessary  elaboration  of  the  author's 
meaning.  It  may  be  enough  for  the  author  to  remark 
that  there  was  a  cupboard  in  the  corner.  He  need  not 
concern  himself  about  what  sort  of  cupboard  it  is;  but 
the  artist  must  make  it  some  definite  kind  and  shape 
of  cupboard.  He  must,  in  fact,  elaborate  the  idea. 
Some  artists  go  in  for  far  more  detail  than  do  others,  but 
in  every  case  they  must  go  into  greater  detail  than  the 
author,  wherever  space  relations  are  involved.  Certain 
artists  show  great  skill  in  giving  just  the  right  amount 
of  detail,  and  in  suggesting  the  rest.  Others  lean  rather 
to  the  methods  of  Walt  Whitman,  and  provide  a  series 
of  elements  in  their  spatial  relations  so  that  the  content 
of  the  description  may  be  made  out  without  any  effort 
on  the  part  of  the  spectator. 

Since  young  people  are  necessarily  in  need  of  as  much 
detail  as  can  be  communicated  to  them  without  undue 
strain,  there  can  be  no  harm  in  using  pictures  copiously 
in  teaching.  Naturally,  it  is  desirable  that  the  idea  of 
the  picture  as  a  whole  should  be  the  true  idea,  so  that  in 
the  future  the  pupil  may  not  have  to  unlearn  anything. 
The  exceptionally  capable  pupil  may  occasionally  re- 
sent the  restraint  on  his  imagination  imposed  by  the 
artist's  work.  But  the  average  pupil,  so  far  from 
resenting  the  artist's  guidance,  feels  grateful  for  combi- 
nations of  ideas  that  he  could  not  have  made  for  him- 
self. Not  only  does  the  picture  supply  combinations, 
it  gives  the  elements  as  well.  By  the  very  fact  that  the 
artist  is  compelled  to  fill  his  space,  he  has  to  introduce 
many  details  that  do  not  appear  in  the  text  at  all.  It 
would  be  intolerably  tedious  to  state  in  writing  a  great 
many  things  that  the  artist  can  represent  by  a  few 


THE  PICTURE  AS  ILLUSTRATION  347 

strokes.  It  is  easy  for  the  artist  to  depict  in  a  few 
square  inches  of  book  space  what  would  take  pages  of 
descriptive  writing  to  set  down  in  a  much  less  effective 
way.  Further,  it  is  much  easier  for  the  pupil  to  interpret 
the  picture  than  the  text.  By  a  mere  glance  he  gathers 
in  a  harvest  of  the  eye  that  could  hardly  under  any 
circumstances  be  gathered  from  reading.  It  is  a 
healthy  sign  that  teachers  are  now  paying  great  atten- 
tion to  the  pictures  in  the  text-books.  Formerly,  it 
was  assumed  that  the  pictures  were  the  children's 
affair;  they  were  regarded  as  mere  attractions,  things 
to  please  the  pupils.  Now  teachers  use  the  pictures  as. 
an  integral  part  of  the  lesson.  In  many  cases,  indeed, 
the  picture  becomes  the  core  of  the  lesson.  In  com- 
position, for  example,  a  picture  is  often  chosen  as  the 
basis  of  a  story  or  explanation.  But  this  is  obviously 
not  a  case  of  illustration.  The  picture  is  being  used 
for  its  own  sake,  and  not  in  relation  to  something  else 
upon  which  it  casts  light.  Frequently  a  picture  that 
was  meant  by  the  artist  to  illustrate  one  thing  may  be 
used  by  the  teacher  to  illustrate  another.  Such  pic- 
tures as  "  The  Derby  Day  "  and  "  The  Railway  Station," 
that  were  meant  by  the  painter  (W.  P.  Frith,  who,  by 
the  way,  began  his  career  as  an  illustrator  of  the  Eng- 
lish classics)  to  illustrate  the  humours  of  his  time,  may 
be  used  by  the  teacher  as  illustrations  of  the  dress  and 
general  background  of  English  life  in  the  middle  of  last 
century. 

We  have  seen  that  all  pictures  are  more  or  less  ab- 
stract. As  a  matter  of  fact,  we  may  arrange  pictures  in 
a  regular  series  of  classes  of  ever  increasing  abstract- 
ness,  till  in  the  final  resort  we  reach  a  stage  that  is  not 
really  pictorial  at  all,  but  diagrammatic.  It  is  impos- 


348    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

sible  to  draw  a  hard  and  fast  line  between  the  picture 
and  the  diagram,  for  there  is  really  a  long  series  of  de- 
grees of  abstractness  from  the  all  but  complete  repre- 
sentation of  an  actual  object  or  scene  at  the  one  end, 
to  the  complete  reduction  to  one  class  of  relations  at 
the  other. 

The  necessary  and  sufficient  mark  of  the  picture  is 
that  it  seeks  to  reproduce  the  object  as  it  appears  to  the 
eye.  The  diagram,  on  the  other  hand,  isolates  certain 
relations,  and  by  isolating  emphasises  them,  and  thus 
frees  them  from  complication  with  others.  Generally 
speaking,  the  picture  may  be  said  to  deal  with  things 
as  they  appear,  the  diagram  with  things  as  they  are. 
The  picture  works  by  appealing  to  suggestion;  the 
diagram  seeks  to  eliminate  suggestion  altogether,  or,  if 
it  makes  use  of  suggestion,  limits  it  strictly  to  one 
particular  line  of  action. 

The  abstractness  of  an  ordinary  picture  is  made  clear 
when  we  consider  the  conventional  element  in  drawing 
and  painting.  We  are  apt  to  think  that  what  we  call  a 
true  reproduction  of  nature  necessarily  conveys  to  the 
human  mind  the  impression  of  the  original.  To  many 
it  seems  superfluous  to  write  and  publish  such  a  book  as 
Mr.  Robert  Clermont  Witt's  How  to  Look  at  Pictures. 
But  here  we  have  160  large  pages  of  print  explaining 
what  is  usually  taken  for  granted.  Pictures  are  gener- 
ally supposed  to  be  self-interpreting,  at  any  rate  in  so 
far  as  they  reproduce  scenes  or  objects  from  the  real 
world.  Yet,  leaving  out  of  account  the  technicalities 
of  the  schools,  there  remains  the  fact  that  we  have  in 
the  most  literal  sense  to  learn  how  to  look  at  pictures. 
Psychologists  have  found  that  illiterate  and  savage 
people  do  not  at  all  understand  what  is  meant  by  a 


THE  PICTURE  AS  ILLUSTRATION  349 

given  picture.  They  have  a  grain  of  salt  for  the  story 
of  the  Greek  artist  Zeuxis,  who  painted  some  cherries 
so  naturally  that  the  birds  came  and  pecked  at  them. 
In  the  case  of  the  savages  of  Borneo,  it  has  been  found 
that  they  do  not  recognise  the  portrait  of  a  man  as  a 
man  at  all,  to  say  nothing  of  being  a  likeness  of  a  par- 
ticular man.1  It  is  clear  that  we  read  into  our  pictures 
more  than  is  actually  there. 

The  picture-maker  must  vary  his  method  according  as 
his  purpose  is  to  give  aesthetic  satisfaction  or  to  impart 
knowledge.  It  is,  of  course,  possible  for  a  picture  to  do 
both;  but  for  purposes  of  illustration  the  informative 
side  is  of  more  consequence.  So  soon,  however,  as  the 
purely  informative  aspect  dominates,  there  is  a  danger 
of  serious  damage  to  the  other.  A  glacier  painted  by 
an  artist  for  his  own  satisfaction  and  the  pleasure  of 
his  patrons  is  a  very  different  thing  from  the  glacier 
painted  to  illustrate  a  geological  lecture.  When  Mes- 
sieurs Lecerf  and  Petit  let  themselves  loose  on  their 
cartoons  for  teaching  La  Morale  par  Exemple 2  the  ar- 
tistic conception  and  execution  are  hardly  worthy  of  the 
fine  lessons  they  teach.  On  the  other  hand,  it  is  quite 
possible  for  the  artistic  sense  to  have  too  free  play  for 
the  results  to  have  any  informative  value.  Such  illus- 
trations as  those  of  Cruikshank  have  no  doubt  an 
illustrative  value.  They  illustrate  the  spirit  of  the 
text.  They  owe  whatever  charm  they  possess  to  their 
whimsical  suggestiveness.  But  on  the  informative  side 

1  Dr.  C.  S.  Myers  tells  me  that  this  does  not  apply  to  the  higher  of 
the  two  grades  into  which  the  Borneans  whom  he  has  studied  are 
clearly  classifiable.     See  also  G.J.Romanes:   Mental  Evolution  in 
Man,  p.  188. 

2  Collection  publiee  sous  la  direction  de  M.  Edouard  Petit,  Inspecteur 
General  de  I' Instruction  Publique. 


350    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

they  are  worse  than  useless.  The  figures  are  unnatural, 
not  to  say  impossible.  But  the  reader  is  willing  to 
accept  them  in  connection  with  a  certain  class  of  book, 
and  to  interpret  the  text  by  then*  means.  They  are  a 
sort  of  humorous  diagram.  We  feel  that  if  they  have  a 
place  anywhere  it  is  in  the  pages  of  Dickens;  hi  Scott 
they  are  objectionable. 

On  the  purely  informative  side,  illustrative  pictures 
leave  as  little  as  possible  to  the  mind  of  the  observer. 
Suggestion  must  be  called  into  play;  but  only  the 
most  obvious  suggestion  is  used.  The  real  is  not  here 
sacrificed  to  the  phenomenal.  The  illustration  of  ad- 
vertisement gives  examples  of  this  sort.  At  any  of  our 
railway  stations  may  be  seen  pictures  of  the  removal 
vans  used  by  various  firms.  In  most  cases  the  vans 
are  drawn  in  an  impossible  position.  They  are  repre- 
sented with  their  long  sides  parallel  to  the  picture  plane, 
which  is  very  convenient,  since  the  printing  on  the  sides 
of  the  van  can  thus  appear  exactly  as  in  a  book,  without 
the  disadvantage  of  foreshortening.  On  the  end  of  the 
van,  naturally,  the  printing  should  appear  to  vanish 
towards  the  centre  of  vision.  The  advertisers  probably 
are  perfectly  aware  of  this,  but  as  foreshortened  print- 
ing is  not  so  emphatic  as  the  straightforward  kind,  they 
prefer  clearness  of  printing  to  accuracy  of  drawing, 
and  simply  represent  the  end  of  the  van  as  if  it  also  were 
parallel  to  the  picture  plane.  No  great  harm  is  done. 
The  ordinary  observer  is  not  at  all  concerned  with  the 
breach  of  the  rules  of  perspective.  This  I  have  tested 
by  more  than  one  hundred  separate  enquiries.  Experi- 
ence shows  that,  when  questioned  as  to  whether  there 
is  anything  wrong  with  the  poster,  the  ordinary  intel- 
ligent observer  makes  some  comment  or  other,  either 


THE  PICTURE  AS  ILLUSTRATION  351 

about  the  kind  of  printing,  the  colour  of  the  poster,  or 
the  removal-conditions  quoted,  —  all  of  which  is  a  full 
justification  of  the  practical  wisdom  of  the  advertiser, 
whose  business  it  is  to  remove  furniture  and  not  to 
educate  the  public.  Obviously,  the  teacher  must  take 
another  view. 

This  desire  to  combine  the  picture  element  with 
the  diagrammatic  has  led  to  the  invention  of  the  iso- 
metric mode  of  projection.  The  draughtsman  wishes 
to  suggest  the  appearance  of  the  object  as  a  whole, 
and  yet  does  not  want  to  give  up  the  advantage  of 
drawing  to  scale  and  making  measurements  from  his 
drawing.  Accordingly,  he  has  hit  upon  the  plan  of 
drawing  all  his  horizontal  lines  at  an  angle  of  thirty 
degrees  with  the  horizontal  edge  of  the  paper,  and  thus 
always  presenting  a  corner  projection  of  the  object  in 
such  a  way  as  to  look  not  altogether  unlike  the  real 
object,  and  at  the  same  time  to  allow  the  draughtsman 
to  make  measurements  on  and  from  his  drawing. 

The  compromise  here  effected  in  the  interests  of 
utility  is  paralleled  by  a  compromise  effected  in  the 
interests  of  art  in  the  Eastern  monumental  reliefs. 
The  Assyrian  Bulls,  if  looked  at  full  in  front,  show  up  a 
pair  of  forelegs,  just  as  we  would  find  if  we  viewed  a  real 
bull  from  this  standpoint;  and  if  the  relief  is  looked  at 
from  the  side,  four  legs  are  seen,  just  as  would  be  the 
case  if  we  observed  from  the  side  a  bull  in  the  act  of 
walking.  If,  now,  the  observer  takes  a  mean  advantage 
of  the  old  sculptor  and  looks  at  the  relief  bull  from  a 
point  midway  between  the  front  and  the  side,  he  sees 
the  animal  with  five  legs.  As  an  inf  ormative  illustration 
this  bull  is  a  failure,  but  as  an  artistic  production  it  has 
the  advantage  of  preserving  the  illusion  of  naturalness 


352  EXPOSITION    AND  ILLUSTRATION  IN  TEACHING 

from  the  two  most  important  points  of  view,  the  front 
and  the  side. 

The  pictorial  series,  in  order  of  increasing  abstract- 
ness,  may  be  thus  summarised :  — 

(1)  Realistic  pictures  hi  which  nothing  is  left  to  the 
imagination  but  the  work  of  combining  the  elements 
supplied,  i.e.  in  interpreting  the  lines  and  colours  ac- 
cording to  the  ordinary  conventions,  so  as  to  call  up 
the  impression  of  the  actual  object  or  scene. 

(2)  Conventional    pictures  hi  which  the  elements 
must  be  combined  according  to  a  more  or  less  arbitrary 
but  intelligible  convention.     To  this  class  belong  ex- 
amples of  the  more  outre    schools  of   painting   that 
require  special  training   to   understand.     Lead   glass 
work  in  ecclesiastical  decoration  would  clearly  belong 
to  this  class. 

(3)  Diagrammatic  pictures  in  which  various  more  or 
less  mechanical  conventions  are  recognised.     To  this 
class  belong  such  drawings  as  those  worked  on  the  iso- 
metric system,  or  any  similar,  recognised  system. 

(4)  Diagrams   in  which  the  drawing  is  not  in  the 
ordinary  sense  quite  like  the  object  represented,  but 
corresponds  to  it  in  certain  points.     Plans  and  eleva- 
tions, for  example,  are  not  really  like  the  objects,  and 
yet  as  they  correspond  to  them  in  space  relations  they 
may  be  said  to  resemble  them.     To  this  class  also  be- 
long all  manner  of  maps,  and  that  large  class  of  draw- 
ings that  in  biological  and  other  scientific  text-books 
are  labelled  "diagrammatic."     These  drawings  retain  a 
certain  resemblance  to  the  original  objects,  but  the 
draughtsman  has  taken  the  liberty  of  suppressing  what- 
ever elements  he  has  found  it  inconvenient  to  intro- 
duce.   The  main  purpose  of  this  kind  of  diagram  is  to 


THE  PICTURE  AS  ILLUSTRATION  353 

divide  and  conquer.  In  dealing  with  the  vascular 
system,  for  example,  it  is  a  positive  disadvantage  to 
have  the  diagram  loaded  up  with  details  of  the  nervous 
system.  There  is  a  place  for  the  nervous  system  by 
itself,  and  also  along  with  the  vascular.  But  this  com- 
bined presentation  belongs  to  a  different  stage  of  teach- 
ing. This  class  of  diagram  does  suggest  the  real  ap- 
pearance of  the  objects  represented,  but  only  in  a  vague 
way.  The  vagueness  is  no  disqualification,  for  the 
general  appearance  of  the  object  is  not  at  this  stage 
important. 

(5)  The  final  stage  is  reached  when  we  come  to  those 
diagrams  in  which  we  have  one  fact  represented  by 
another  with  which  it  has  no  apparent  connection. 
The  two  are  wholly  disparate,  save  in  respect  of  the 
one  element  in  which  they  are  compared.  There  is  no 
connection,  for  example,  between  a  straight  line  and 
the  amount  of  wool  exported  from  Australia,  and  yet 
the  varying  state  of  the  export  trade  in  wool  may  be 
well  illustrated  by  a  series  of  lines  of  different  lengths. 


2A 


CHAPTER  XV 
THE  DIAGRAM 

THE  relation  between  the  picture  and  the  diagram 
as  means  of  illustration  may  be  brought  out  by  a 
consideration  of  the  relation  between  the  easy  and  the 
simple  in  teaching.  These  two  terms  are  sometimes 
taken  to  be  synonymous.  But  everything  depends 
upon  the  stage  the  pupils  have  reached  in  the  subject 
under  discussion.  We  have  seen  that  while  a  generalisa- 
tion is  simpler  than  the  mass  of  details  from  which  it  has 
been  drawn,  it  is  easier  only  to  those  who  have  mastered 
the  details,  and  thus  earned  their  generalisation.  So 
with  graphic  illustration.  Speaking  generally,  the  dia- 
gram is  simpler  than  the  picture,  and  yet  the  picture 
is  in  most  cases  easier  than  the  diagram.  If  we  follow 
the  principle  from  the  simple  to  the  complex,  it  would 
seem  that  we  ought  to  begin  with  the  diagram  and  rise 
to  the  picture.  The  teacher,  however,  is  driven  to 
reverse  the  process,  if  only  to  be  consistent  with  the 
other  teaching  principle,  from  the  concrete  to  the 
abstract.  We  have  here  a  practical  example  of  an  only 
too  prevalent  tendency  to  pit  one  principle  against  an- 
other in  an  unintelligent  way.  So  soon  as  we  take  a 
wide  enough  view,  we  find  that  the  two  principles  are 
quite  consistent. 

In  point  of  fact,  the  place  of  the  picture  is  both  at  the 
beginning  and  the  end  of  a  process  of  teaching.  At  the 

354 


THE  DIAGRAM  355 

beginning  it  gives  a  general  idea  of  the  whole  with 
which  we  are  dealing.  This  can  be  grasped  in  a  more 
or  less  vague  way.  There  then  ought  to  follow  a  study 
in  greater  detail,  in  which  certain  elements  have  to  be 
treated  by  themselves.  Here  the  diagram  is  obviously 
in  place,  and  may  be  used  with  whatever  degree  of 
abstractness  is  required.  When  the  detailed  study  has 
been  completed  for  that  particular  stage,  the  picture 
should  once  more  be  introduced  to  gather  up  the  pupil's 
new  knowledge  and  fit  it  into  its  proper  place.  In  each 
teaching  unit  involving  graphic  illustration  we  should 
begin  with  the  picture,  and  end  with  the  picture.  All 
between  is  the  domain  of  the  diagram. 

Yet  so  strong  is  the  power  of  the  picture  that  it 
remains  immanent  throughout  the  process,  and  is  ready 
at  any  moment  to  obtrude  itself.  A  diagram  seems  to 
have  an  inherent  tendency  to  acquire  content  and 
become  a  picture.  Since  the  value  of  the  diagram  is 
its  abstractness,  it  is  clear  that  a  loss  of  abstractness 
is  a  loss  of  the  virtue  of  the  diagram  as  such,  except  in  so 
far  as  the  pictorial  element  is  consistent  with  the  dia- 
grammatic. The  general  sense  of  the  solidity  of  the 
heart  that  obtrudes  itself  upon  the  flat  diagrammatic 
representation  of  it  does  not  in  any  way  hinder  the 
diagram  in  its  illustrative  work.  But  if  we  are  dealing 
diagrammatically  with  a  question  of  quantity,  and  the 
picture  element  introduces  the  question  of  quality, 
the  pictorial  influence  is  prejudicial. 

This  is  well  shown  in  some  of  the  popular  methods  of 
diagrammatic  representation.  It  is  now  fashionable  to 
represent  quantities  pictorially  rather  than  diagram- 
matically in  the  strict  sense  of  the  latter  term.  For 
instance,  it  is  desired  to  convey  a  vivid  impression  of  the 


356    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

amount  of  tobacco  smoked  in  his  lifetime  by  a  man  who 
consumes  so  many  cigars  per  week.  This  is  supposed 
to  be  best  represented  by  a  drawing  in  which  the  cigar 
bears  the  same  ratio  to  the  man  that  the  weight  of  to- 
bacco consumed  during  the  man's  lifetime  bears  to  his 
own  weight.  Accordingly,  a  manikin  is  represented 
with  an  enormous  cigar  in  his  mouth.  No  doubt  the 
area  of  the  cigar,  as  represented  by  square  centimetres, 
has  the  same  ratio  to  the  area  of  the  man  in  the  same 
denomination  as  the  number  of  pounds  of  cigar  has  to 
the  number  of  pounds  of  man.  But  while  we  have  thus 
an  appearance  of  mathematical  accuracy,  the  only 
effect  produced  upon  the  observer  is  the  impression 
that  the  man  smoked  a  very  great  number  of  cigars. 
On  the  whole,  the  statement  in  words  of  the  number  of 
pounds  of  tobacco  and  the  number  of  pounds  the  man 
weighed  would  convey  a  clearer  idea  of  the  situation 
than  the  diagram  does.  It  is  commonly  said  that  the 
illustration  is  much  more  interesting  when  put  in  the 
pictorially  diagrammatic  way.  But  the  gain  in  interest 
is  at  the  expense  of  relevancy.  The  sizes  of  the  armies 
of  Europe  may  be  represented  by  a  series  of  soldiers 
dressed  in  the  uniform  of  the  respective  countries, 
each  soldier  being  made  of  a  certain  size,  according  to 
some  standard,  so  as  to  represent  the  size  of  the  army 
of  his  country.  The  resulting  impression  is  not  at  all 
clear.  It  is  complicated  in  two  ways. 

In  the  first  place,  we  have  the  introduction  of  quality 
where  it  has  no  place.  While  we  are  considering  the 
size  of  the  armies  of  Russia  and  Italy,  we  have  nothing 
to  do  with  the  peculiar  cast  of  countenance  of  a  Russian 
or  an  Italian;  yet  these  qualities  are  thrust  upon  our 
notice  in  the  drawing.  No  doubt  the  appearance  of  the 


THE   DIAGRAM  357 

men,  their  uniforms,  and  their  weapons  are  of  the  utmost 
consequence  in  considering  the  value  of  the  various 
armies.  But  this  particular  diagram  is  used  to  illus- 
trate only  the  one  element  of  size.  The  rest  may  be 
illustrated  in  various  ways.  Some  parts  of  the  whole 
illustrandum  may  be  best  represented  pictorially,  as,  for 
example,  the  weapons  and  accoutrements;  but  wherever 
statistical  elements  alone  are  involved,  the  pure  diagram 
will  be  found  to  be  most  serviceable,  and  least  apt  to 
convey  false  impressions. 

The  second  source  of  complication  in  the  pictorial 
diagrams  is  the  introduction  of  the  element  of  area. 
If  the  mere  height  of  the  soldiers  represents  the  size  of 
the  army,  then  clearly  a  series  of  straight  lines  would, 
for  illustrative  purposes,  serve  better  than  the  pictured 
figures.  But  if  the  numerical  proportion  of  the  armies 
to  one  another  is  represented  by  the  area  covered  by 
the  figure  of  the  soldier,  then  a  very  serious  difficulty  is 
introduced.  The  ordinary  reader  can  compare  straight 
lines  with  very  little  difficulty.  But  the  comparison  of 
areas  is  beyond  him.  Anyone  who  has  not  given  the 
matter  attention  will  be  surprised  at  our  general  weak- 
ness in  estimating  area.  We  are  all  singularly  feeble 
in  the  matter  of  comparing  the  relative  sizes  of  surfaces, 
and  in  particular  in  correlating  lengths  with  areas. 
We  can  compare  two  lines  with  each  other  with  a  fair 
chance  of  justly  estimating  their  ratio,  but  few  among 
us  can  make  even  a  reasonable  guess  at  the  relative 
areas  of  two  given  circles  or  squares.  To  prove  how 
easily  we  may  be  misled  in  comparing  lines  with  areas, 
ask  any  friend  who  has  not  had  the  experiment  already 
imposed  upon  him  how  many  cent  pieces  or  " pennies" 
we  can  place  flat  on  the  surface  of  a  silver  dollar  without 


358    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

any  one  of  them  overlapping,  however  slightly,  the  cir- 
cumference of  the  larger  coin.  The  ordinary  answer 
varies  from  three  to  five.  The  fact,  however,  is  that 
even  two  of  the  little  copper  coins  are  more  than  the 
dollar  can  receive  on  its  surface  under  these  conditions. 


FIG.  5. 


Take  two  small  coins,  say  quarters,  and  place  them  on  a 
table  at  such  a  distance  from  each  other  as  you  think 
will  leave  room  for  one  other  quarter  to  fit  in  exactly 
between  the  two.  When  you  have  tested  your  result, 
you  will  probably  find  that  you  are  considerably  wrong 
in  your  calculation,  and  that  any  friend  with  whom 
you  experiment  goes  wrong  in  the  same  direction  as 
yourself.  You  are  really  trying  to  determine  the  length 
of  the  diameter,  but  the  area  of  the  coin  leads  you  into 


THE   DIAGRAM  359 

error.  Our  weakness  is  shown  also  in  our  inability  to 
guess  correctly  without  previous  practice  the  height  in 
inches  of  a  silk  hat  resting  on  its  crown.  Further,  take 
two  pieces  of  paper  and,  putting  the  one  above  the  other, 
cut  out  in  duplicate  the  shape  indicated  in  figure  5. 
You  will  then  have  two  pieces  of  paper  of  exactly  equal 
area,  but  if  you  place  them  one  below  the  other,  as  in 
figure  5,  you  will  find  it  very  difficult  not  to  maintain 
that  the  lower  of  the  two  is  greater  than  the  upper. 

Psychologists  supply  us  with  many  examples  of  false 
impressions  conveyed  with  regard  to  areas,  lengths, 
and  directions,  and  one  would  almost  think  makers  of 
diagrams  deliberately  selected  modes  of  representation 
that  illustrate  certain  of  the  psychologists'  illusions.1 

It  is  customary  to  represent  the  areas  of  countries 
and  continents  by  a  series  of  squares  or  triangles;  and 
at  first  sight  it  may  appear  plausible  to  maintain  that, 
since  we  are  illustrating  areas,  the  best  illustration  is 
surely  other  areas.  It  may  even  be  asked,  if  we  cannot 
compare  intelligently  little  areas,  like  printed  triangles 
and  squares,  what  hope  is  there  that  we  can  compare 
areas  like  those  of  continents  and  countries  ?  Now  it 
has  to  be  admitted  frankly  that  most  of  us  have  no  real 
conception  of  what  is  meant  by  the  hundreds  of  thou- 
sands of  square  miles  that  we  read  about  in  our  geog- 
raphy text-books.  But  it  is  one  thing  to  know  a  mat- 
ter absolutely,  and  another  to  know  it  relatively.  It  is 
one  thing  to  know  what  is  meant  by  the  statement  that 
North  Carolina  contains  52,250  square  miles,  and  an- 
other to  realise  that  its  area  is  a  little  over  twenty-five 

1  Lightner  Witmer,  in  his  Analytical  Psychology,  Chap.  Ill,  par- 
ticularly pp.  86-98,  gives  some  exceedingly  interesting,  and  from  the 
teacher's  standpoint  most  instructive,  illustrations. 


360    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 


times  that  of  Delaware.  We  may  not  be  able  to  realise 
the  vast  extent  of  country  implied  by  these  figures,  but 
we  may  be  able,  by  comparison  with  a  smaller  state  (in 
this  case  Delaware)  with  which  we  are  assumed  to  have 
a  much  better  acquaintance,  to  make  certain  practical 
applications  of  the  statement  of  the  larger  area.  If  we 
have  a  standard  area1  that  we  really  know  by  having 
walked  or  driven  over  great  parts  of  it,  we  may  on  that 
basis  build  up  a  scale  which  we  can  intelligently  use. 
The  bigger  the  available  unit  the  better.  An  additional 
advantage  follows  when  the  pupil  is  able  to  compare 
by  actual  inspection  a  smaller  unit  than  his  standard, 
so  as  to  determine  how  many  times  this  smaller  unit  is 
included  in  the  standard  unit.  If,  for  example,  in  this 
particular  case  the  pupil  who  lives  in  Delaware  has  had 

a  chance  of  running 
over  Rhode  Island, 
which  has  more  than 
half  the  area  of  Dela- 
ware and  Connec- 
ticut (more  than 
double  the  Delaware 
area),  he  will  find  his 
standard  (Delaware) 
much  more  useful 
for  purposes  of  com- 
parison. 

But  granting  the 
standard,  there  re- 
mains the  question  of  the  best  means  of  graphically 
representing  the  unit  and  its  multiples.  Here  the  text- 
books are  again  in  favour  of  reduced  areas.  North 

1  See  p.  315. 


FIG.  6. 


THE   DIAGRAM 


361 


FIG.  7. 


Carolina  is  represented  by  a  square  of,  say,  2|-inch 
side,  and  in  the  corner  the  area  of  Delaware  is  repre- 
sented by  a  square  of  |-inch  side.  If  the  two  squares 
are  left  thus,  they  do 
not  give  a  very  clear 
impression  of  the  rela- 
tive sizes  of  the  two 
states.  It  is  found  by 
experiment  that  a  class 
gets  a  better  compari- 
son between  the  two 
squares  in  figure  6  if 
the  sides  of  the  larger 
square  are  marked  off 
into  five  equal  parts, 
and  still  better  if  the 
whole  square  is  marked  off  into  twenty-five  squares 
of  the  Delaware  size,  as  in  figure  7. 

From  the  ordinary  atlas  the  pupil  is  apt  to  get  a  dis- 
torted view  of  the  relative  sizes  of  the  countries  of  the 
world.  Each  country  and  continent  has  a  map  to  itself 
on  a  sheet  of  its  own,  so  that  North  America,  Germany, 
and  Scotland  all  appear  to  be  of  the  same  size,  the 
only  help  the  pupil  gets  being  the  little  scale  of  miles 
that  he  is  very  apt  to  overlook.  Wall  maps  have  the 
same  defect.  Some  publishers  adopt  the  reasonable 
plan  of  inserting  in  the  corner  of  maps  that  are  drawn 
to  a  very  small  scale  a  little  outline  map  of  some  stand- 
ard country  drawn  to  the  same  scale.  Thus,  the  state 
in  which  the  pupil  lives  might  well  appear  in  the  corner 
of  maps  of  the  continents,  India,  China,  Australia, 
and  the  United  States.  To  illustrate  the  relative  sizes 
of  the  countries  of  Europe  an  ingenious  teacher  first 


362    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 


COMPARATIVE  VIEW  OF  THE  AREAS 
OF  THE  CONTINENTS,  REDUCED 
TO  SQUARES. 


made  a  tracing  of  the  whole  continent  from  the  wall 
map,  then  he  coloured  each  of  the  countries  with  a  flat 
wash,  next  he  cut  out  all  the  countries  and  mounted 
Russia  on  a  sheet  of  paper  that  just  comfortably  re- 
ceived it.  After  this  he  got  a  series  of  sheets  of  paper 

of  the  exact  size  used 
to  mount  Russia,  and 
pasted  on  each  of  them 
one  of  the  other  coun- 
tries of  Europe.  The 
amount  of  white  margin 
in  the  case  of  small  coun- 
tries like  Denmark  and 
Belgium  certainly  em- 
phasised then*  relative 
poverty  of  area. 

The  accompanying 
diagram,1  figure  8,  rep- 
resents an  attempt  to 
illustrate  the  areas  of 
the  continents.  It  is 

found  in  practice  to  be  of  very  little  service.  In  order 
to  test  its  utility,  I  experimented  in  several  towns  with 
many  classes  of  pupils  of  various  ages  from  12  upwards. 
The  area  of  one  of  the  continents  was  given,  and  the 
problem  set  was  to  estimate  from  the  diagram  what  the 
areas  of  the  other  continents  were.  The  answers  were 
very  wide  of  the  mark,  and  certain  interesting  varia- 
tions were  observed.  The  worst  results  were  obtained 
when  the  area  supplied  was  that  of  Australia;  the  next 

'John  Macturk:  Elementary  Physical  Geography,  p.  317. 
1  Reproduced  by  kind  permission  of  Messrs.  William  Collins,  Sons 
and  Co.,  London  and  Glasgow. 


.AFRICA 

AFRICA 

NORTH  AMER 

CA 

NORTH  AMERICA 

SOUTH  AMERICA 

SOUTH  AMERICA  1 

EUROPE 

• 
c 

g 

TJ 

AUSTRALIA 

FIG.  8.2 


THE  DIAGRAM 


363 


worst  when  Asia  was  the  standard;  the  best  results 
followed  when  either  North  or  South  America  formed 
the  starting-point.  Classes  that  had  studied  mensura- 
tion did  better  than  those  that  had  not.  I  was  able 
to  eliminate  the  difference  in  age,  for  I  managed  to  get 
four  classes  of  boys  of  the  same  age,  two  of  which  had 
studied  mensuration  and  two  had  not.  A  further  pecu- 
liarity was  that  when  the  diagram  was  put  hi  the  form  of 
a  series  of  six  squares  standing  outside  of  each  other,  and 
arranged  in  order  of  size,  the  results  were  better  than 
when  the  squares  were  so  placed  as  to  have  one  angle 
common.  The  explanation  is  probably  that  when  the 
squares  were  superimposed  there  was  greater  "interfer- 
ence" in  the  sense  that  term  bears  when  used  in  physics. 

Conspicuously  better  results  were  obtained  when  two 
of  the  six  areas  were  given,  the  best  results  of  all  being 
obtained  when  Europe  and  Africa  were  the  continents 
selected  as  standards,  though  Asia  and  Australia  made 
a  combination  that  had  results  very  little  inferior. 

In  point  of  fact,  however,  the  following  table  that 
accompanies  the  diagram  in  Mr.  Macturk's  book  gives  a 
more  useful  presentation  than  does  the  diagram:  — 

SIZE  OF  THE  CONTINENTS  (INCLUDING  ISLANDS)' 


GREATEST 
LENGTH 

GREATEST 
BREADTH 

AREA  IN  SQ. 
MILES 

COMPARATIVE 
SIZE 

Europe     .     .     . 

3400m. 

2450  m. 

3,700,000 

1 

Asia     .... 

6700m. 

5400m. 

16,400,000 

41 

Africa  .... 

5000m. 

4600m. 

11,100,000 

3 

N.  America  .     . 

5600m. 

3120  m. 

7,600,000 

2 

S.  America   .     . 

4500m. 

3000m. 

6,800,000 

U 

Australia  .     .     . 

1900m. 

2400m. 

3,000,000 

I 

Take  Europe  as  the  standard  of  comparison. 


364    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

In  the  table  the  areas  are  given  in  sufficiently  round 
numbers  to  admit  of  easy  comparison  with  each  other, 
a  comparison  that  is  further  aided  by  the  "compara- 
tive size"  column.  It  would  be  well,  however,  as  a 
matter  of  presentation  that  the  continents  should  be 
arranged  in  the  table  in  regular  ascending  or  descending 
order  of  size  to  match  the  diagram.  Taken  along  with 
the  table,  the  diagram  may  be  said  to  be  helpful;  but 
if  the  teacher  has  to  choose  between  the  comparative 
size  column  and  the  diagram,  he  will  be  well  advised 
to  give  up  the  diagram.  The  illustrandum  being  the 
column  of  "area  in  square  miles,"  the  comparative 
size  column  will  certainly  be  a  better  illustration  than 
is  the  diagram.  When  a  class  is  confronted  with  the 
squares  in  figure  8  without  any  indication  that  they 
represent  continents,  the  pupils  are  found  to  be  inca- 
cable  of  estimating  the  relative  areas  of  the  squares. 
Given  the  area  of  the  Europe  square  as  100,  only 
two  out  of  a  class  of  75  postgraduate  students  esti- 
mated with  reasonable  correctness  the  areas  of  the  re- 
maining five.  Eighteen  of  them  estimated  the  largest 
square  as  between  700  and  800.  The  general  impres- 
sion produced  by  the  students'  estimates  was  that  the 
diagram  by  itself  confused  rather  than  helped. 

Still  less  hopeful  is  the  accompanying  diagram,  figure 
9.  The  wider  circle  has  an  area  one  hundred  times  as 
great  as  has  the  small  black  circle  in  the  centre.  As 
the  total  area  of  the  United  States,  including  Alaska, 
is  3,617,384  square  miles,  and  the  area  of  Indiana  is 
36,350  square  miles,  the  diagram  might  be  used  to  illus- 
trate the  relation  between  the  area  of  this  state  and  the 
area  of  the  whole  republic.  The  diagram  is  supposed 
to  make  the  ratio  clearer  than  does  the  mere  statement 


THE   DIAGRAM 


365 


of  the  figures.  As  a  matter  of  fact,  the  statement  that 
the  one  area  is  almost  exactly  a  hundred  times  the  other 
conveys  a  much  clearer  idea  than  does  the  presentation 
of  the  diagram.  Pupils  are  unable  to  estimate  the 
ratio  between  the  two  circles.  I  have  made  this  the 


FIG.  9. 

subject  of  experiment  by  placing  a  large  copy  of  the 
diagram  drawn  to  scale  before  about  thirty  classes  of 
pupils  between  12  and  15  years  of  age  (representing 
altogether  1245  individual  pupils)  without  giving  any 
hint  about  what  it  represented  geographically.  The 
only  question  asked  was :  How  many  times  is  the  big 
circle  bigger  than  the  little  one?  I  made  the  same  test 
with  various  classes  of  undergraduate  students  (453  in- 


366    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 


dividual  students  in  all)  of  ages  19  to  22.  The  follow- 
ing is  the  percentage  results  of  the  estimates  formed 
by  the  various  pupils :  — 


GROUP  I 

GROUP  II 

Pupils  12-15 

Pupils  19-22 

Under  100  

56.2 

30.1 

Exactly  100     

15.7 

290 

Over  100     . 

28.1 

40.9 

100.0 

100.0 

Naturally  the  older  pupils  made  fewer  wild  guesses 
than  the  juniors.  In  Group  1, 17.2  per  cent  estimated 
the  area  as  under  20  times;  in  Group  II,  only  2.3  per 
cent  made  this  low  estimate.  But  strangely  enough, 
while  of  Group  I  only  8.0  per  cent  estimated  over  300 
times,  9.3  per  cent  of  Group  II  made  this  exaggerated 
estimate.  One  striking  difference  between  the  two 
groups  is  that  there  is  much  more  " round  number" 
work  among  the  first  Group.  The  second  Group  quite 
obviously  deals  with  squares  of  numbers,  while  the  first 
Group  have  exactly  50.7  per  cent  of  even  number  guesses 
—  i.e.  20,  30,  40,  ...  200,  300,  400,  etc.,  up  to  1000. 
In  Group  I  2.5  per  cent  estimate  exactly  1000.  Only 
one  student  in  Group  II  makes  this  loose  guess.  In  the 
first  Group  one  pupil  guesses  5000,  and  one  actually 
goes  the  length  of  10,000.  The  great  majority  of  the 
guesses  are,  in  fact,  quite  wild.  About  a  dozen  pupils 
in  Group  I  give  such  inexplicable  answers  as  "They  are 
as  big  as  each  other."  But  a  good  many  must  have 
thought  what  one  pupil  had  the  courage  to  write: 


THE  DIAGRAM  367 

"One  cannot  tell  how  much  bigger,  as  the  small  one  can 
go  into  it  almost  as  many  times  as  one  likes." 

In  the  case  of  Group  II  it  appears  likely  that  29  per 
cent  represents  the  real  proportion  of  those  who  esti- 
mated 100  correctly.  The  same  can  hardly  be  said 
for  Group  I.  The  tendency  to  select  round  numbers 
is  so  marked  that  we  must  make  allowance  for  the  in- 
clination to  be  specially  attracted  to  100  because  it  is 
so  preeminently  a  round  number.  Thus,  while  15.7  per 
cent  guessed  100  exactly,  no  fewer  than  12.04  per  cent 
guessed  50  exactly,  while  5.5  per  cent  guessed  200 
exactly. 

The  important  result  of  the  experiments  from  the 
point  of  view  of  Illustration  is  that  the  diagram  gives 
no  real  help  in  estimating  the  relative  sizes  of  two  geo- 
graphical areas.  Can  it  be  maintained  that  the  illus- 
tration works  the  other  way?  If  the  pupils  are  unable 
to  estimate  that  the  big  circle  is  a  hundred  times  bigger 
than  the  little  one,  are  they  at  all  likely  to  be  clearer 
about  the  ratio  of  1  to  100  by  looking  at  the  diagram 
after  being  told  what  the  ratio  is?  If  not,  can  the  dia- 
gram be  said  to  serve  any  useful  purpose?  The  answer 
would  appear  to  be  that,  taken  in  connection  with  the 
actual  figures,  there  may  be  a  certain  aesthetic  satis- 
faction in  seeing  the  diagram.  It  may  therefore  help 
in  fixing  an  impression  that  is  made  by  other  means, 
but  its  effect  must  be  recognised  to  be  aesthetic,  not 
didactic. 

Geometricians  discriminate  between  what  they  call 
diagrams  of  illustration  and  metrical  diagrams.  The 
first  kind 

"  are  intended  to  help  the  reader  to  follow  the  mathematical  rea- 
soning. The  construction  of  the  figure  is  defined  in  words  so 


368    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

that  even  if  no  figure  were  drawn  the  reader  could  draw  one  for 
himself." 1 

The  second  kind  are 

"employed  in  an  entirely  different  way  —  namely,  for  purposes 
of  measurement.  The  plans  and  designs  drawn  by  architects  and 
engineers  are  used  to  determine  the  value  of  certain  real  magni- 
tudes by  measuring  certain  distances  on  the  diagram."1 

The  diagrams  we  have  just  been  dealing  with  must 
be  regarded  as  more  or  less  illegitimate  examples  of  the 
metrical  kind.  No  doubt  they  are  used  to  illustrate 
certain  relations,  and  these  relations  are  of  a  purely 
quantitative  nature.  On  the  other  hand,  they  are  not 
set  out  so  that  measurements  may  be  taken  from  them. 
No  doubt  we  could  calculate  from  them  the  relations 
they  illustrate,  but  this  is  certainly  not  the  function 
they  were  introduced  to  perform.  Rather  are  they 
called  upon  to  illustrate  calculations  that  have  already 
been  made.  They  are,  in  fact,  a  hybrid  between  the 
two  classes. 

In  spite  of  the  literal  meaning,  —  "marked  out  by 
lines,"  —  the  term  diagram  may  be  applied  to  drawings 
in  which  colour  plays  an  essential  part.  The  areas  in  the 
drawing  may  indicate  one  set  of  facts,  while  the  colours 
that  are  washed  in  over  the  areas  may  indicate  another. 
The  areas  may,  for  example,  indicate  quantitative  re- 
lations, the  colours  qualitative.  In  a  geological  map 
the  extent  of  the  various  strata  is  indicated  by  the  area 
set  apart  for  each,  while  the  nature  of  the  strata  is 

,  *  How  far  this  is  true  of  the  ordinary  reader  may  be  tested  by 
asking  some  one  to  read  the  Meno,  82-85,  from  a  text  without  a  dia- 
gram, and  then  make  an  illustrative  diagram  to  suit.  Few  indeed  will 
be  able  to  supply  what  is  wanted. 

*  J.  Clark  Maxwell,  in  the  Ency.  Brit.,  ninth  ed.  Vol.  VII,  p.  149. 


THE  DIAGRAM  369 

indicated  by  the  colours :  black  may  indicate  coal;  yellow, 
chalk;  red,  volcanic  rocks;  and  so  on.  It  is  to  be  noted 
that  here  we  have  another  example  of  the  immanence 
of  the  picture  in  the  diagram.  There  is  a  natural  con- 
nection between  black  and  coal,  and  between  red  and 
the  rocks  that  are  produced  by  fire.  The  same  feeling 
after  the  pictorial  is  seen  in  the  maps  illustrating  the 
various  levels  of  the  different  parts  of  the  earth's 
surface.  It  is  a  natural  convention  to  represent  the 
low-lying  lands  by  different  shades  of  green  according 
to  their  height,  the  higher  mountainous  levels  by 
various  shades  of  brown  (points  above  the  snow-line 
being  left  white),  and  the  sea  by  varying  shades  of  blue. 
But  colours  may  be  used  in  a  completely  abstract  way, 
as  in  the  case  in  which  exports  and  imports  are  repre- 
sented by  different  colours. 

Sometimes  colours  and  areas  are  combined  for  illus- 
trative purposes.  When  this  is  done,  there  should  be 
the  greatest  care  in  maintaining  consistency  in  the  use 
of  the  colours.  In  a  diagram  lying  before  me  as  I  write, 
there  are  two  circles,  each  divided  up  into  sectors 
representing  the  amounts  of  the  imports  and  exports 
of  Great  Britain  from  and  to  various  countries.  Here 
each  country  should  retain  the  same  colour  in  both  cir- 
cles. But  I  find  that  France  is  green  in  the  imports 
and  salmon-coloured  in  the  exports ;  Holland  is  salmon- 
coloured  in  the  imports  and  blue  in  the  exports;  Russia 
is  yellow  in  the  exports  and  blue  in  the  imports.  It 
may  be  thought  that  change  in  the  colours  is  a  trifling 
matter;  but  somehow  colour  has  a  great  attraction  for 
all  of  us,  and  particularly  for  young  people.  Nothing 
can  be  called  trifling  that  draws  attention  in  the  wrong 
place  and  suggests  difference  where  none  exists. 

2B 


370    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

A  favourite  method  of  representing  statistical  facts  is 
by  means  of  columns  of  varying  height.  The  method 
is  excellent,  but  it  must  be  used  with  certain  restrictions. 
First,  the  element  of  area  must  be  eliminated.  The 
columns  must  be  of  uniform  width,  so  that  the  real 
measurement  is  made  in  height.  In  several  diagrams 
I  have  examined  I  have  found  that  when  very  large 
numbers  have  to  be  used  along  with  small  numbers,  the 
columns  representing  the  bigger  numbers  are  so  tall  that 
it  is  impossible  to  include  them  in  the  page.  Accord- 
ingly they  are  broken  up  into  strips  and  placed  side  by 
side.  No  objection  need  be  taken  to  this  so  long  as 
the  strips  are  of  uniform  length.  Six  such  strips  would 
naturally  make  a  biggish  rectangle,  and  would  there- 
fore represent  a  very  large  number,  but  the  largeness  of 
the  number  would  be  estimated  by  the  number  of  strips, 
not  by  the  area  of  the  rectangle.  Sometimes  the  mis- 
take is  made  of  representing  a  quantity  that  is  just  too 
big  for  a  single  strip  by  two  equal  strips,  each  a  little 
bigger  than  half  a  standard  strip.  This  is  a  blunder, 
for  in  this  case  we  are  driven  to  deal  with  area  and  not 
merely  with  length.  The  quantity  should  be  repre- 
sented by  a  complete  standard  strip  and  a  little  bit  of 
an  additional  strip.  Each  column  is,  in  fact,  treated  as 
a  line,  and  the  complex  diagram  is  really  made  up  of  a 
series  of  lineal  measurements.  We  judge  by  the  heights 
of  the  various  columns,  and  thus  get  a  good  general 
idea  of  the  comparative  importance  of  the  different 
quantities.  When  it  comes  to  accurate  details,  we  must 
fall  back  upon  the  actual  figures,  which  are  usually 
available.  As  a  rule  it  is  not  wise  to  use  illustrations 
of  this  kind  as  metrical  diagrams. 

Psychologically,  it  is  not  quite  accurate  to  say  that 


THE  DIAGRAM  371 

columns  may  be  treated  merely  as  lines.  Our  estimate 
of  the  width  of  columns  is  affected  by  the  relative  heights 
of  the  columns  compared.  A  low  column  appears  wider 
in  proportion  to  a  high  column  of  the  same  real  width. 
But  this  peculiarity  need  not  interfere  with  the  use  of 
columns  as  illustrations  of  statistical  relations  in  one 
denomination.  So  long  as  we  have  a  standard  height 
and  a  uniform  width,  we  can  treat  them  merely  as  thicker 
lines  than  usual.  A  particularly  useful  form  of  colum- 
nar diagrams  is  that  in  which  squared  paper  is  used  as  the 
groundwork,  and  squares  are  blackened  so  as  to  form 
columns  of  various  heights.  Each  column  is  in  this 
case  so  many  squares  high,  and  the  "permanent  sug- 
gestion" of  the  squareness  of  the  unit  prevents  the 
question  of  breadth  arising;  though  it  must  be  ad- 
mitted that  in  the  case  of  a  fraction  of  a  square  being 
filled  up  at  the  top  of  a  column  there  is  danger  of  a 
trifling  disturbance  through  the  breadth  bias. 

While  it  is  true  that  quantities  are  better  represented 
by  straight  lines  *  than  by  areas,  there  is  the  limitation 
that  when  there  is  a  great  disparity  between  the  two 
quantities  compared,  the  mind  may  be  unable  to  make 
the  comparison.  If,  instead  of  the  squares  in  figure  7, 
we  draw  a  line  one  inch  long  to  represent  the  area  of 
Delaware,  and  another  twenty-five  inches  long  to 
represent  North  Carolina,  it  will  be  discovered  that 
pupils  find  it  impossible  to  make  an  accurate  estimate 

1  In  connection  with  the  view  that  the  straight  line  is  the  funda- 
mental form  of  quantitative  illustration,  my  friend,  Dr.  William  Gar- 
nett,  the  eminent  physicist,  refers  to  the  fact  that  in  physics  all  meas- 
urements are  ultimately  reduced  divisions  of  a  line.  The  galva- 
nometer, the  thermometer,  the  barometer  all  exemplify  this.  Even 
in  the  balance  the  line  remains  the  standard,  though  in  this  case  it 
is  reduced  to  zero. 


372    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

of  the  relation  between  the  two  areas.  In  such  cases 
the  line  must  be  broken  up  in  some  way,  so  that  the 
ratio  may  be  made  manifest.  One  writer  who  wishes 
to  represent  by  means  of  straight  lines  the  ratio  between 
the  trade  of  the  British  Isles  and  the  trade  of  the  vari- 
ous British  colonies,  represents  the  British  trade  by  a 
line  so  long  hi  proportion  to  the  others  that  he  has  to 
fold  it  into  what  may  be  described  as  a  spiral  rectangle 
that  has  rather  more  than  two  and  a  half  whorls. 
Then  this  rectangle  is  filled  with  other  lines  variously 
folded.  The  perverted  ingenuity  of  the  plan  may  be 
gathered  from  its  application  in  figure  10  to  the  areas 
of  various  states  of  the  Union.  The  plain  statement 
of  the  facts  is:  — 

Rhode  Island 1,250  square  miles. 

Maryland 12,210  square  miles. 

Kentucky 40,400  square  miles. 

New  York 49,220  square  miles. 

Illinois 56,650  square  miles. 

Texas 265,780  square  miles. 

This  is  contorted  into 


fLUNOIS 

MARYLAND 

RHODE  iStXNO 
KENTUCKY 

NEW  YORK 

FIG.  10. 


THE  DIAGRAM  373 

Two  principles  should  be  kept  in  view  when  we  are 
dividing  up  a  line  so  as  to  use  it  effectively  in  quantita- 
tive illustration.  The  first  is  that  we  should  always 
work  in  multiples  of  the  smallest  line  to  be  included. 
Thus,  in  the  area-of-North-Carolina  illustration  (figure 
7,  page  361),  we  should  divide  the  twenty-five  line  into 
five  lines,  each  five  times  the  length  of  the  line  represent- 
ing the  area  of  Delaware.  Had  we  been  dealing  with 
the  state  of  New  York,  which  is  almost  exactly  twenty- 
four  times  the  area  of  Delaware,  we  would  divide  the 
longer  line  into  four  parts,  each  six  times  the  Delaware 
length.  Naturally,  if  there  is  not  a  convenient  multiple 
to  include  all  that  we  want  without  leaving  anything 
over,  than  we  must  adopt  the  nearest  multiple  and 
represent  the  remainder  by  a  proportionately  smaller 
length.  If  the  bigger  state  were  represented  by  the 
number  twenty-six  (Arkansas,  with  53,850  square  miles, 
fits  in  here  almost  exactly),  we  might  either  take  nine 
as  the  multiple  and  give  two  full  lines  and  eight-ninths 
of  another,  or  take  five,  as  before,  and  add  a  fifth  of  an- 
other. 

The  second  principle  is  that  we  should  arrange  our 
rows  of  multiple  lines  horizontally  rather  than  vertically, 
as  it  is  found  that  the  eye  works  more  easily  from  side 
to  side  than  up  and  down. 

It  is  probable  that  it  is  this  difficulty  in  dealing  in 
terms  of  straight  lines  with  widely  different  quantities 
that  has  led  to  the  introduction  of  illustrations  by  areas. 
These  give  a  wider  range,  without  the  need  of  trouble- 
some foldings  or  duplications.  Rectangular  areas  seem 
to  lend  themselves  more  readily  to  subdivision  than  do 
circular  areas.  But  this  does  not  prevent  the  enter- 
prising illustrator  from  using  the  circle.  Indeed,  this 


374    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

form  of  illustration  is  at  present  rather  in  favour.  A 
circle  is  taken  to  represent  some  total,  and  is  divided 
up  into  various  sectors,  each  representing  a  specific 
part  of  this  total.  But  here,  again,  it  is  very  difficult  to 
estimate  the  areas  of  the  sectors.  The  usual  way  is  to 
make  an  estimate  of  the  relative  areas  of  the  various 
sectors  by  comparing  the  parts  of  the  circumference  cut 
off  by  the  including  radii.  Considerable  skill  in  estimat- 
ing angular  measurement  may  be  acquired  by  a  study 
of  the  face  of  the  clock  and  the  different  positions  of 
the  hands.  Limiting  himself  to  the  positions  of  the 
twelve  hours,  the  student  assumes  the  unit  of  the  hour 
as  equivalent  to  30°,  and  by  estimating  the  position 
of  the  radii  in  relation  to  the  fixed  points  of  the  hours, 
he  can  make  a  fair  guess  at  the  number  of  degrees 
included,  and  therefore  of  the  proportion  of  the  area 
of  the  circle  included  in  a  given  sector. 
The  two  following  diagrams  were  published  in  an 


FlQ.    11. 


official    document   to   illustrate    certain    quantitative 
relations.     One  would  have  thought  that  the  percent- 


THE  DIAGRAM  375 

ages  required  no  help,  but  somehow  the  drawings  were 
assumed  to  make  the  matter  clearer,  till  one  of  the  offi- 
cials, who  had  trained  his  eye  on  the  clock-face 
standard,  chanced  to  see  them,  and  declared  after  a 
moment's  inspection  that  both  were  incorrect  (a)  to 
the  extent  of  two-thirds  of  an  hour  (i.e.  10°)  and  (6) 
to  the  extent  of  one-third  of  an  hour  (i.e.  5°).  On 
measurement,  the  reader  will  find  that  the  estimate  is 
almost  exactly  right,  so  skilful  is  it  possible  to  become 
at  estimating  angular  measurement  by  reference  to  a 
fixed  standard.  It  is  true  that  this  is  not  quite  an 
estimate  of  areas,  but  rather  of  positions  on  a  circle. 
The  estimate  of  the  included  area  is  really  an  inference 
from  the  angular  measurement.  This  last  fact  has 
probably  something  to  do  with  the  popularity  of  the 
circular  form  of  quantitative  illustration. 

Sometimes  the  circular  diagram  is  used  in  a  way 
that  depends  still  less  on  the  area-sense.  The  state  of 
a  particular  business  of  some  complexity,  or  of  some 
government  department,  in  a  given  year  is  represented 
by  an  inner  circle.  Each  succeeding  year  is  represented 
by  an  outer  concentric  circle,  and  the  increase  or  dimi- 
nution in  certain  elements  (sales,  cases,  prosecutions, 
deaths,  or  what  not)  is  indicated  by  the  protrusion  of 
larger  or  smaller  extensions  of  uniform  shape,  but  vary- 
ing size,  from  the  original  circle.  If  the  concentric 
circles  increase  by  a  uniform  lengthening  of  radius  each 
year,  the  protrusions  from  the  original  circle  may  be 
compared  with  each  other  on  the  same  standard,  so  long 
as  their  shape  does  not  depend  on  the  diameter  of  the 
circles.  Oblong  protrusions  of  uniform  width  may 
press  into  any  number  of  concentric  circles  without 
being  affected  by  the  increasing  diameters.  We  are,  in 


376    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

fact,  enabled  to  treat  the  oblong  prolongations  as  mere 
lines.  Ingenious  people,  of  course,  can  introduce  all 
manner  of  more  or  less  useful  complications.1 

It  may  very  reasonably  be  questioned  whether  the 
general  weakness  that  we  have  observed  in  estimating 
areas  is  an  essential  part  of  human  nature.  It  may 
well  be  that  this  is  merely  a  department  of  experience 
that  has  not  received  its  proper  share  of  attention.  Ed- 
ucation has  certainly  done  little  towards  training  this 
particular  mode  of  dealing  with  the  materials  presented 
by  the  outside  world.  Experiments  have  been  made,  it 
is  true,  but  seldom  on  a  large  scale,  or  continued  for  a 
long  time.  Several  years  ago  an  enthusiast  in  educa- 
tion in  the  east  of  Scotland  produced  a  scheme  for  the 
training  of  all  our  sense  perceptions.  On  the  analogy 
of  Athletics,  he  called  his  system  "Menties."  It  was 
not  widely  taken  up,  but  in  one  or  two  cases  it  was 
applied  with  great  thoroughness  and  success.  An  es- 
sential part  of  the  scheme  was  a  training  in  the  estimat- 
ing of  areas,  and  in  one  case,  at  least,  in  which  it  was 
applied  the  pupils  developed  quite  a  striking  skill  in 
estimating  areas  that  happened  to  fall  into  the  geo- 
metrical forms  that  had  been  used  in  their  training. 
That  is  to  say,  the  pupils  could  readily  arrange  in  order 
of  area  a  number  of  cardboard  hexagons,  triangles, 
squares,  and  other  regular  figures.  They  were  less 
happy  in  arranging  in  order  figures  that  had  not  occurred 
in  their  regular  exercises,  but  they  did  much  better 
work  even  with  irregular  figures  than  any  class  of 
equally  intelligent  but  untrained  pupils.  On  the 

1  For  a  very  interesting  example  of  this  form  of  circular  illustration, 
see  the  Report  of  the  Minister  of  Public  Instruction  of  New  South 
Wales,  1908.  (Physical  Condition  of  Children.) 


THE  DIAGRAM  377 

other  hand,  when  the  "mentically"  trained  pupils  were 
taken  into  the  country,  they  showed  no  unusual  skill 
in  estimating  in  acres  the  fields  through  which  they 
passed;  though  looking  at  clearly  marked  fields  from 
a  height  at  some  distance,  they  were  able  to  compare 
with  fair  accuracy  the  areas  of  the  different  fields. 

There  can  be  no  doubt  but  that  under  the  rapidly 
approaching  development  of  handwork  in  all  its 
branches  in  schools  the  area-sense  will  be  much  more 
highly  cultivated  than  in  the  past,  and  even  the  bulk- 
sense  will  receive  a  certain  amount  of  training.  In  the 
meantime,  it  is  very  difficult  to  get  an  ordinary  pupil  to 
understand  how  a  fifty-cent  microscope  can  be  said, 
without  actual  lying,  to  magnify  " nearly  30,000  times," 
while  a  fifty-dollar  instrument  claims  no  more  for 
itself  than  four  or  five  hundred  times,  or  seven  hundred 
at  the  most.  We  may  point  out  to  the  pupil  that  the 
first  is  estimated  in  cubical  content  and  the  second 
in  diameters.  But  after  we  have  explained  that  the 
cheaper  microscope  probably  magnifies  30  diameters, 
or  900  (i.e.  30  x  30)  area  units,  or  27,000  (i.e.  30  x  30 
x  30)  cubic  units,  the  pupil  still  finds  a  difficulty  in 
taking  in  our  meaning.  To  be  fair  to  the  good  micro- 
scope, we  must  claim  that  it  magnifies  343,000,000  tunes 
(700  x  700  x  700).  But  this  seems  to  prove  too  much. 
The  pupil  clearly  thinks  he  is  being  imposed  on.  This 
enormous  figure,  he  thinks,  must  be  a  mere  "way  of 
talking"  —  and  he  is  right.  As  a  matter  of  fact,  ex- 
cept on  the  smallest  scale,  we  cannot  perceive  cubical 
content ;  we  must  deal  with  it  as  a  matter  of  inference. 
We  are  all  familiar  with  the  very  common  confusion 
between  eight  feet  square  and  eight  square  feet.  But 
confusion  is  much  more  general  when  we  deal  with 


378    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

cubic  content.  Most  people  who  are  preparing  for 
their  first  ocean  voyage  make  a  very  serious  error  in 
their  interpretation  of  the  "  twenty  cubic  feet/'  or  the 
"sixty  cubic  feet"  allowed  for  baggage.  Their  minds 
are  dazzled  by  a  spaciousness  hi  which  an  additional 
trunk  or  two  are  matters  of  no  moment.  Some  people 
never  acquire  the  volumetric  sense,  but  have  through- 
out life  to  take  the  shipping  people's  word  for  the 
surcharge.  Others  are  amenable  to  the  teachings  of 
experience,  and  come  to  form  a  fair  idea  of  what  the 
phrase  "sixty  cubic  feet"  means  when  expressed  in 
crates  and  trunks.  But  while  this  form  of  inference 
may  be  trained,  the  process  is  a  part  of  substantive 
teaching,  and  ought  to  precede  the  use  of  the  area-  or 
volumetric-sense  as  an  aid  in  illustrating  something 
else.  Diagrammatic  illustration  offers  a  capital  field 
for  the  sense  when  cultivated,  but  is  not  the  field  in 
which  the  cultivation  should  take  place. 

Pending  the  further  development  of  the  area-sense, 
it  will  be  wise  to  limit  the  range  of  the  diagrammatic. 
Since  the  great  value  of  the  diagram  is  its  abstractness, 
it  does  not  seem  desirable  to  carry  it  into  a  region 
where  extraneous  elements  have  to  be  taken  into 
account.  If  we  can  represent  all  we  want  by  means  of 
straight  lines,  why  should  we  seek  for  a  more  complicated 
medium  ?  When  we  know  that  Indiana  is  only  one- 
hundredth  part  of  the  area  of  the  whole  of  the  states, 
why  should  we  seek  for  illustrations  that  only^  hamper 
our  freedom  in  dealing  with  this  fact?  After  all,  it  is  a 
quantitative  fact,  and  should  not  be  confounded  with  a 
qualitative  one.  It  is  true  that  after  we  have  mastered 
this  mere  numerical  ratio,  we  have  a  very  great  deal  to 
learn  before  we  can  apply  this  knowledge  intelligently. 


THE  DIAGRAM  379 

Mere  area  is  not  everything.  But  the  necessary 
amplification  of  our  knowledge  is  to  be  brought  about 
by  other  forms  of  illustration.  We  shall  understand 
the  meaning  of  Indiana  and  the  United  States  a  little, 
but  not  much,  better  because  we  have  learnt  that  a 
certain  white  circle  is  one  hundred  times  as  big  as  a 
certain  black  one.  What  is  wanted  after  that  is  an 
application  of  the  principle  of  elaboration.  So  far  as 
mere  quantity  is  concerned,  we  have  enough  when  we 
have  the  bald  statement  of  the  ratio. 

One  of  the  best  illustrations  of  the  application  of  the 
Jacototian  principle,  "Learn  one  thing  thoroughly  and 
refer  everything  else  to  it,"  is  to  be  found  in  a  diagram 
(figure  12)  that  occurred  in  the  geography  book  1  on 
which  I  exhausted  my  boyish  enthusiasm.  Unfortu- 
nately, my  teacher  did  not  attend  to  the  NOTE  at  the 
foot.  The  diagram  was  always  taken  for  granted,  so 
that  a  large  number  of  my  classmates  never  quite 
knew  what  was  meant  by  the  remarks  that  headed  the 
various  countries  dealt  with  in  the  text.  For  example, 
under  PERU,  one  read  "  Latitude  in  the  middle  the  same 
as  the  south  of  Lower  Guinea";  and  under  ARABIA, 
"Same  latitude  as  from  the  middle  of  Morocco  to  the 
middle  of  Senegambia."  In  schools,  however,  where 
the  book  is  properly  used  (for  it  has  still  a  wide  sale), 
there  is  continual  reference  to  the  diagram,  with  the 
result  that  the  pupils  learn  to  know  exceedingly  well 
the  relative  positions  of  the  different  countries  on  the 
face  of  the  globe.  Naturally,  this  is  not  the  final  stage 
in  teaching  relative  position  on  the  earth's  surface. 
It  represents  the  pictorial  stage,  or  perhaps,  better,  the 
pictorial  aspect.  There  is  not  only  room,  but  necessity, 

1  Modern  Geography  for  the  Use  of  Schools,  by  Robert  Anderson. 


380    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 


NOTE.  —  Teachers  are  requested  to  see  that  their  pupils  thoroughly  master 
this  brief  lesson.  The  position  of  these  eleven  countries,  which  occupy  the 

western  shores  of  the  Old  World,  is  used  to  indicate  the  latitude  of  all.  other 
countries  of  the  globe. 

FIG.  12.» 


1  Reproduced  by  kind  permission  of  Messrs.  Thomas  Nelson  and 
Sons,  London  and  New  York. 


THE  DIAGRAM  381 

for  the  freer  indication  of  position  on  the  surface  of  the 
globe  as  indicated  by  latitude  and  longitude.  But  the 
diagram  follows  the  laws  of  good  teaching  in  beginning 
with  the  matter  and  ending  with  the  form.  A  similar 
diagram  of  the  Eastern  states  might  be  used  with  very 
great  advantage  in  teaching  the  relative  positions  of  the 
various  parts  of  the  Union.  When  we  are  given  the 
latitude  and  longitude  of  Georgia  and  Oregon,  we  can,  by 
referring  to  a  common  standard  reason  out  their  rela- 
tive positions.  But  in  facts  that  are  so  close  to  our 
everyday  life  it  is  well  to  get,  wherever  possible,  at 
immediate  connections.  If  we  fix  the  position  of  a  given 
state,  by  reference  to  a  certain  state  on  the  Eastern 
coast,  we  are  working  up  our  complex  of  the  states  as  a 
whole. 

Speaking  generally,  a  diagrammatic  illustration  should 
be  reduced  to  its  lowest  possible  terms.  Caran  d'Ache, 
Phil  May,  and  other  artists  who  dazzle  us  by  the  fewness 
of  their  lines,  seek  quite  a  different  effect  from  that 
proper  to  the  diagram.1  Their  aim  is  to  reach  the  maxi- 
mum of  suggestiveness  with  the  minimum  of  representa- 
tion. They  invite  the  spectator  to  supply  as  full  details 
as  he  can,  and  their  success  is  measured  by  the  con- 
trast between  the  exiguous  presentation  and  the  ex- 

1  We  are  told  that  such  artists  make  their  first  drawings  in  the 
ordinary  way,  filling  in  all  the  details  so  as  to  get  a  broad  general  effect. 
Then  they  proceed  to  discover  which  lines  are  essential,  and  by  a  grad- 
ual process  of  elimination  they  reach  the  effective  skeleton  that  is 
finally  reproduced.  The  same  thing  is  true  of  writing.  Mr.  H.  G. 
Wells,  for  example,  tells  us  that  he  first  writes  down  things  as  they 
come  into  his  mind,  so  as  to  "get  some  idea  of  the  shape  of"  his 
subject.  This  first  writing  he  calls  "slush,"  and  it  is  ruthlessly  cut 
down  as  the  book  approaches  completion.  The  "slush"  may  amount 
to  over  100,000  words,  the  completed  book  to  55,000.  (Interview 
in  To-day,  Sept.  11,  1897). 


382    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

uberant  mental  picture.  The  diagram,  on  the  other 
hand,  seeks  to  confine  the  attention  to  one  particular 
direction.  It  seeks  to  illustrate  one  relation.  Caran 
d'Ache  invites  to  an  exercise  in  elaboration,  the  dia- 
gram to  an  exercise  in  elimination.  A  curious  illustra- 
tion of  this  invitation  to  elaboration  was  supplied  some 


189* 
1890 

FIG.  13. 

years  ago  when  there  was  a  passing  fashion  in  what  was 
called  " match-drawing."  This  consisted  in  represent- 
ing human  beings  by  means  of  straight  lines  only,  as  a 
child  might  do  by  placing  matches  on  a  table,  so  as  to 
represent  the  trunk,  legs,  and  arms.  The  interesting 
point  for  us  is  the  skill  with  which  the  draughtsmen 
could  suggest  characteristic  attitudes  with  this  very 
limited  means  of  expression.  Fencers,  boxers,  walkers, 
runners,  were  all  reproduced  in  the  penny  illustrated 
magazines  in  such  a  way  that  the  spectator  had  to  fill 
in  the  details  whether  he  would  or  no.  Sometimes 
match-drawing  is  used  for  real  illustration.  Thus,  in 
a  journal  called  Cycling,  on  July  22,  1894,  there  ap- 
peared the  preceding  drawing,  figure  13,  to  illustrate  the 
difference  of  the  attitude  in  riding  the  bicycle  in  the 
year  1890  and  in  the  year  1894.  It  appears  that  be- 


THE  DIAGRAM  383 

tween  these  two  dates  a  lamentable  degeneration  had 
taken  place,  owing  to  the  scorching  habit.  It  is  to  be 
hoped  that  the  accompanying  sketches  represent  an 
exaggeration:  what  we  are  certain  of  is  that  they  viv- 
idly represent  the  views  of  the  magazine  writer.  The 
reader's  attention  is  not  distracted  by  the  personal 
appearance  of  the  riders,  or  the  qualities  of  the  machines. 
Only  the  essentials  appear. 

There  is  a  certain  amount  of  complication  involved 
here,  since  suggestion  will  naturally  invite  to  poten- 
tial elaboration.  One  may  read  as  much  anatomy  and 
physiology  and  fashion  into  the  figures  as  one's  know- 
ledge admits.  But  there  is  not  a  line  in  the  illustration 
that  can  be  fairly  called  non-essential.  We  have  here 
practically  reached  the  limits  of  suggestion  by  resem- 
blance in  a  diagram. 

There  remains  that  kind  of  diagram  that  represents 
certain  truths  without  indicating  any  sort  of  resem- 
blance between  the  lines  and  forms  used  and  the  con- 
tent of  the  complex  that  forms  the  illustrandum.  All 
the  newer  graphic  methods  used  in  the  teaching  of 
mathematics  belong  to  this  class,  and  all  the  various 
schemes  of  plotting  out  results  in  charts.  The  ac- 
companying diagram,  figure  14,  for  example,  has  no  re- 
semblance to  either  work  or  fatigue,  yet  it  represents 
in  a  very  efficient  way  the  relation  between  fatigue 
effect  and  practice  effect  in  determining  the  amount  of 
intellectual  work  done  in  a  given  time.  The  abscissa, 
OM,  represents  the  length  of  time  the  test  lasted,  in 
this  case  two  hours.  The  ordinate,  OL,  represents 
the  amount  of  work  done.  The  work  begins  at  A,  and 
for  a  little  time,  through  distraction  and  the  effort  to 
concentrate,  there  is  a  slight  diminution  of  efficiency  in 


384    EXPOSITION   AND  ILLUSTRATION   IN   TEACHING 


work.  At  B  the  practice  effect  begins  to  tell,  and  the 
line  gradually  rises  to  C.  At  this  point  the  practice 
effect  is  counterbalanced  by  the  fatigue  effect  that  goes 


O  LENGTH  OF  TIME  THE  TEST   LASTED!  IN  THIS  CASE  TWO  HOURS       M 

Fio.  14.1 

on  increasing,  while  the  practice  effect  cannot  increase 
further.  The  result  is  that  there  is  a  gradual  falling  off 
in  the  effectiveness  of  the  work  till  we  reach  D.  Here 
the  prospect  of  a  speedy  release  from  effort,  along  with 
a  quickening  of  the  conscience,  in  view  of  the  approach- 
ing end  of  further  opportunity,  gives  a  little  fillip  to  the 
student,  and  his  effectiveness  rises  somewhat  till  the 
two  hours  end  at  E* 

The  value  of  such  diagrams  is  that  we  can  envisage  at 
one  glance  a  large  number  of  facts  that  would  baffle 
any  mind  to  deal  with  when  presented  seriatim. 
What  Professor  Karl  Pearson  calls  an  "  observation 
frequency  polygon," 3  and  Mr.  Graham  Wallas  (from  a 

1  Reproduced  by  kind  permission  of  Messrs.  Schleicher  Freres, 
Paris. 

*  A.  Binet  and  V.  Henri :  La  Fatigue  Intellectuelle,  p.  239. 

3  For  illustrations,  see  the  periodical  Biometrika,  passim,  or  Karl 
Pearson's  Chances  of  Death. 


THE  DIAGRAM  385 

vague  memory  of  its  shape)  calls  a  "cocked  hat,"1  is 
one  of  the  best  examples  of  this  graphic  aid  to  think- 
ing. Mr.  Wallas  quotes  from  Professor  Marshall 2  in 
support  of  the  statement  that  qualitative  reasoning  in 
economics  is  passing  away  and  quantitative  reasoning  is 
beginning  to  take  its  place.3  Among  my  postgraduate 
(science)  students,  many  of  whom  have  studied  under 
Professor  Karl  Pearson,  and  most  of  whom  have  been 
influenced  by  him,  I  note  an  increasing  tendency  to 
think  in  diagrams.  I  come  across  this  line-thinking 
in  all  manner  of  unexpected  places.  An  essay  on  the 
Shakespeare-Bacon  controversy  was  full  of  "cocked 
hats,"  and  in  an  essay  handed  in  the  other  day  on  the 
interactions  between  pupil  and  teacher,  I  found  the 
whole  positions  set  out  in  a  sort  of  diagram  of  forces. 

The  now  common  school  plan  of  recording  such 
matters  as  lengths  of  shadows,  temperatures,  baro- 
metric pressures,  school  attendances,  have  rendered 
the  chart  form  of  illustration  familiar  even  to  young 
children.  It  is  true  that  these  records  are  treated 
as  processes  of  instruction  rather  than  of  illustration, 
and  in  the  preparation  of  the  curves  there  is  training 
of  a  very  valuable  kind.  Children  are,  hi  fact,  being 
taught  to  think  quantitatively.  For  our  present  pur- 
pose the  important  point  is  that  pupils  are  now  pre- 
pared by  their  substantive  school  work  to  understand 
all  manner  of  chart  illustrations. 

We  have  seen  already  the  value  of  the  straight  line 

1  Human  Nature  in  Politics,   1908,  p.  133. 

2  Journal  of  Economics,  March,  1907,  pp.  7  and  8. 

3  Human  Nature  in  Politics,  p.  143.     Here  Mr.  Wallas  gives  a  very 
amusing  and  enlightening  illustration  of  quantitative  thinking  on  the 
subject  of  the  best  size  for  a  debating  hall  of  given  shape. 

2c 


386    EXPOSITION  AND  ILLUSTRATION   IN   TEACHING 

as  the  best  way  of  indicating  a  comparison  in  one  single 
element,  as  area,  or  length,  or  cost,  or  weight.  But 
there  is  another  way  in  which  the  straight  line  has  a 
special  illustrative  value.  In  dealing  with  mental 
activity  we  find  that  sense  of  direction  is  character- 
istic of  mental  functioning.  "When  this  'direction'  is 
determined  for  me,"  says  Dr.  James  Ward,  "I  am  said 
to  be  passive;  when  it  is  determined  by  me,  I  am  said 
to  be  active."1  There  appears  to  be  something  more 
than  mere  metaphor  in  this  psychological  use  of  the 
word  direction.  Here  is  what  Professor  S.  Alexander 
has  to  say  on  the  subject:  — 

"  Now  that  I  know  what  my  brain  is,  I  feel  my  thought  occurring 
there,  or,  if  not  there,  in  some  other  part  of  my  body.  It  is  only 
as  thus  understood  in  connection  with  the  bodily  organism  that  I 
can  say  my  mental  activity  is  a  movement  with  direction.  But  in 
this  sense  it  is  a  movement  that  does  occur  in  time  and  space. 
In  other  words,  my  mental  activity  is  always  qualified  by  what,  on 
the  analogy  of  local  signs,  I  must  call  signs  of  direction." 2 

Without  laying  too  much  stress  on  the  psychological 
basis  thus  suggested,  it  may  fairly  be  said  that  the 
straight  line  in  certain  diagrams  performs  the  functions 
of  those  signs  of  direction.  In  a  genealogical  table  the 
lines  really  do  direct  the  mind,  which  in  following  this 
direction  shows  itself  to  be  in  this  case  passive.  It  is  a 
matter  of  common  experience  that  the  mind  is  dominated 
by  arrows  and  other  indications  of  direction  as  they 
appear  in  graphic  form.  That  such  indications  are  a 
saving  of  thought  effort  is  proved  by  their  use  in  the 
graphic  humour  of  the  Sunday  papers,  in  which  it  is 
now  customary  to  indicate  the  direction  of  a  projectile 

1  Proceedings  of  the  Aristotelian  Society,  1908,  p.  226. 
3  Ibid.,  p.  220. 


THE  DIAGRAM 


387 


by  dotted  lines,  so  that  the  indolent  spectator  may  be 
saved  even  the  trifling  trouble  of  discovering  from  which 
direction  the  projectile  came  on  its  fun-making  errand. 
The  plain  man's  desire  "to  see  a  thing  in  black  and 
white"  is  better  met  by  a  linear  diagram  than  in  any 
other  way.  Even  when  the  letterpress  is  perfectly 

THE  TEACHER'S  USE  OF  LANGUAGE. 
THE  BRIDGE 


WHICH 
WILL. 


EXAMPLE. 

DOG  SUGGESTS 

T    FOUR-LEGGEDNE88 

II.  HAIRINESS 

III.  TAILEDNES8 
JV.    TWO-EYEDNES8 

V.    8NOUTEDNE88 
ETC..   ETC. 


FAMILIAR     \f    8OMET|M"Eg 


EXAMPLE. 
OOG  SUGGESTS; 
I.    RETBIEVER 

II.  ST.  BERNARD 

III.  FOX-TERRIER 

IV.  NEWFOUNDLAND 

V.  POODLE 


FIG.  15. 


simple,  the  reader  frequently  likes  to  have  a  diagram- 
matic representation.  In  1903  I  published  a  little 
Primer  on  Teaching  meant  specially  for  Sunday-school 
people.  Naturally  I  wished  to  make  the  text  as  simple 
as  possible,  and  thought  that  I  had  made  it  so  plain 
that  no  one  could  need  any  help  to  understand  its 
meaning.  Some  time  after  its  publication  I  received 
from  a  clever  engineer  *  in  New  York  a  set  of  eleven 
diagrams  that  give  a  graphic  representation  of  the 
main  points  in  the  various  chapters.  The  engineer  was 
the  superintendent  of  a  Sunday-school,  and  told  me 
1  Mr.  John  Calder. 


388    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

that  he  found  his  teachers  understood  the  book  hi  a 
much  more  practical  way  after  he  had  given  them  his 
diagrams.  Figure  15  reproduces  one  of  these  diagrams. 
On  looking  at  it,  one  would  think  that  the  matter 
could  have  been  equally  well  expressed  in  plain  verbal 
exposition.  But  on  putting  the  matter  to  several 
fairly  well-educated  Sunday-school  teachers,  I  found 
that  they,  on  the  whole,  preferred  to  have  the  diagram, 
but  were  good  enough  to  admit  that  it  must  come  after 
the  text. 

We  need  be  the  less  surprised,  then,  to  find  diagrams 
in  such  abstract  books  as  Mr.  W.  MacdougalPs  Social 
Psychology.  In  introducing  an  admirably  clear  exposi- 
tion of  the  neural  bases  of  the  sentiments  of  hate  and 
love  he  says:  "It  is,  I  think,  helpful,  at  least  to  those 
who  make  use  of  visual  imagery,  to  attempt  to  picture 
a  sentiment  as  a  nervous  disposition  and  to  schematise 
it  crudely  by  the  aid  of  a  diagram."  l  As  a  matter  of 
fact,  the  diagram  consists  of  a  row  of  seven  small  circles, 
each  representing  one  of  the  primary  emotional  dis- 
positions. The  rest  consists  merely  of  certain  lines  and 
arrows  indicating  direction.  These  lines  have  a  com- 
pelling power,  and  cause  the  mind  to  follow  them  al- 
most hi  spite  of  itself.  They  are  more  useful  in  help- 
ing the  student  to  understand  than  in  helping  him  to 
recall  details. 

It  has  to  be  noted  that  the  mere  presence  of  the  lines 
helps  to  fix  the  attention.  This  is  the  justification 
of  the  habit  some  capable  teachers  have  of  making 
what  seem  quite  unnecessary  lines  on  the  blackboard. 
They  will  put  down  this  sort  of  thing  on  the  blackboard 
and  accompany  it  by  something  like  the  following: 

1  Social  Psychology,  p.  124. 


THE  DIAGRAM 


389 


"Let  A  represent  Walpole,  B  Queen  Caroline,  and  C 
George  the  Third.  The  natural  way  of  communicat- 
ing with  the  king  would  have  been  for  the  minister  to 
speak  directly  to  him;  but  as  a  matter  of  fact,  impor- 
tant communications  usually  took  the  route  indicated 
by  the  arrows."  All  that  this  triangular  method  im- 

A 

x 

B 


plies  has,  of  course,  to  be  brought  out  by  the  teacher, 
but  he  feels  that  he  has  had  a  greater  grip  on  the  pupil's 
attention  because  of  the  apparently  unnecessary  figure. 
When  I  suggested  to  the  teacher  that  it  might  have  been 
better  to  use  significant  letters,  W,  C,  and  G,  he  main- 
tained— influenced,  no  doubt,  by  his  memories  of  math- 
ematics—  that  the 
more  conventional  the 
symbols  the  better. 
To  put  the  actual 
names  Walpole,  Caro- 
line, and  George  would, 
he  maintained,  have 
spoiled  everything. 
Here  he  differed  from 
the  originator1  of  this 
illustration  —  strangely 
enough  the  teacher  to  whom  I  spoke  seemed  to  re- 
gard the  illustration  as  his  own  —  who  uses  the  signi- 
ficant initials  W,  K,  and  Q.  The  view  that  significant 
letters  are  objectionable  is  evidently  adopted  by  the 
writers  of  the  Public  School  Latin  Primer,  in  which  the 

1R.  Somervell  in  P.  A.  Harriett's  Teaching  and  Organisation,  p.  171. 


FIG.  10. 


390    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

solitary  little  diagram  in  the  book,  figure  16',  illustrates 
case  by  means  of  letters  without  significance :  — 

—  "  Case  (casus,  from  cado)  is,  literally,  a  falling.  Grammarians  rep- 
resented that  form  which  a  Noun  takes  when  it  is  the  Subject  of  a 
sentence  by  an  upright  line,  as  AB,  and  likened  the  other  forms  to 
lines  falling  away  from  the  perpendicular  at  various  angles,  as,  AC, 
AD,  AE,  AF,  etc.  These  they  called  Cases;  and  their  series,  the 
declension,  declining,  or  sloping  down  of  the  word.  Afterwards, 
the  Nominative  or  Subject  case  was  called  (with  evident  impropriety) 
Casus  Rectus,  the  Upright  Case,  and  the  others  (except  the  Voca- 
tive), Casus  Obliqui,  Oblique  Cases;  whereas  the  Stem  (or  Crude  form) 
of  the  word  is  more  properly  the  upright  line,  and  the  several  cases, 
including  the  Nominative  and  Vocative,  are  branches  deflecting 
from  it.  So,  from  the  Stem  nuc-  (walnut-tree),  the  Cases  are :  N.  V., 
nuc-s  (-ux),  Ace.,  nuc-em,  G.,  nuc-is,  D.,  nuc-i,  Ab.,  nuc-e."  l 

Probably  the  influence  of  custom  on  the  schoolmaster 
in  making  "Diagrams  of  Illustration"  in  Euclid  had  a 
good  deal  to  do  with  the  selection  in  this  case  of  the 
first  letters  of  the  alphabet.  At  any  rate,  in  actual 
exposition  to  a  class,  experience  shows  that  it  is  better 
to  adopt  significant  letters.  0  is  substituted  for  A,  and 
S  for  B;  thus,  OS  represents  the  stem;  then  0  Ace.  would 
represent  the  accusative,  OG  the  genitive,  and  so  on. 
It  would  seem  that  the  pupil  can  hardly  understand  the 
meaning  of  case  much  better  from  seeing  his  teacher 
draw  seven  lines  from  a  given  point;  but  in  practice  it 
is  said  that  the  drawing  does  actually  help.  Probably 
some,  at  least,  of  the  advantage  comes  from  the  draining 
off  of  a  certain  amount  of  nervous  energy  on  the  part 
of  both  teacher  and  pupil,  an  energy  that  might  other- 
wise interfere  with  the  learning  process,  just  as  in  think- 
ing out  riders  in  Euclid  the  pupil  works  more  steadily 
when  he  has  a  pencil  in  his  hand,  even  if  he  makes  no 
use  of  it  in  the  way  of  either  drawing  or  writing. 

1  P.  154. 


CHAPTER  XVI 

DANGERS  OF  ILLUSTRATION 

As  an  ending  to  a  question  the  words  "Give  exam- 
ples," are  very  dear  to  the  heart  of  the  examiner. 
With  those  who  are  called  upon  to  write  answers  to  ex- 
amination questions,  the  words  are  not  quite  so  popular. 
The  complaint  of  the  examiners  is  that  the  examples 
given  are  stereotyped.  If  an  example  is  given  in  a 
text-book,  it  reappears  with  cloying  persistency  in  the 
answers.  Out  of  nine  hundred  answers  to  a  question 
in  a  Board  of  Education  school  management  paper 
asking  for  an  example  of  one  word  being  run  into  an- 
other in  reading  aloud,  over  six  hundred  gave  "this 
shrub"  the  actual  phrase  used  in  a  then  popular  text- 
book. Very  few  candidates  had  the  originality  even  to 
change  the  letters  while  retaining  the  actual  example, 
as  in  "  this  stable." 

Experience  shows  that  there  is  a  strong  tendency  to 
fall  into  ruts  in  illustrating  any  particular  point.  Ask 
a  class  for  examples  of  sentences.  If  the  first  pupil 
says  "Cows  eat  grass,"  the  chances  are  that  his  fel- 
lows will  go  on  mentioning  what  other  animals  eat.  If 
we  wish  to  provide  reasonably  varied  examples  for 
class  work,  we  must  consider  beforehand  which  illus- 
trations we  shall  use  in  a  given  lesson.  It  is  the  com- 
monest thing  in  the  world  to  find  a  teacher  depending 
for  his  illustrations  on  the  spur  of  the  moment.  If  he 

391 


392    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

has  a  mind  particularly  well  stored  with  matter  on  the 
subject  he  is  dealing  with,  he  may  escape  from  the  seri- 
ous defect  of  supplying  tiresome  strings  of  more  or  less 
similar  and  eminently  commonplace  examples  of  the 
rules  he  is  expounding.  It  is  easy  enough  to  supply 
almost  unlimited  quantities  of  examples  of  particular 
kinds  of  nouns  and  verbs,  or  of  natural  orders  in  botany, 
or  of  islands  hi  geography.  In  writing  on  the  black- 
board sums  to  be  worked  out,  the  teacher  finds  that  the 
numbers  come  without  the  least  difficulty.  In  all  these 
cases  the  connection  between  the  rule  and  the  example 
is  so  clear  that  no  mistake  is  possible  except  through 
such  culpable  ignorance  as  is  seldom  to  be  found  among 
teachers.  Here  one  example  does  almost  as  well  as 
another.  The  content  of  the  individual  example  does 
not  affect  the  general  rule  to  be  illustrated. 

So  far,  what  may  be  called  the  hand-to-mouth  method 
of  illustration  is  innocuous,  and  is  even  advantageous, 
since  it  saves  unnecessary  labour.  So  soon  as  the  con- 
tent of  the  illustration  becomes  of  importance,  the 
method  will  be  found  to  be  full  of  danger.  The  teacher 
who  carelessly  dictates  at  random  half  a  dozen  English 
sentences  to  be  translated  into  Latin  to  illustrate  the 
construction  of  cum  with  the  subjunctive,  may  lead  to 
all  manner  of  confusion  among  his  pupils,  because  they 
find  in  the  sentences  other  difficulties  than  those  con- 
nected with  cum,  difficulties  that  have  not  been  pre- 
pared for  by  any  previous  instruction.  A  teacher's 
brilliant  scholarship  is  no  safeguard  against  error  here. 
All  such  illustrative  sentences  must  be  carefully  edited 
by  the  teacher  in  the  light  of  what  he  knows  of  the  previ- 
ous training  of  his  pupils.  No  doubt  there  comes  at  a 
later  stage  of  instruction  in  Latin  prose  a  time  when  the 


DANGERS  OF  ILLUSTRATION  393 

pupils  must  be  prepared  to  deal  with  unedited  English 
passages  for  translation  into  Latin;  for  at  that  stage 
they  have  a  sufficiently  wide  knowledge  of  Latin  con- 
struction to  allow  them  to  exercise  a  certain  freedom. 
But  even  at  this  stage  the  master  must  not  select  his 
English  passage  entirely  at  random.  Certain  passages 
cannot  be  translated  into  Latin,  since  they  contain 
words  and  ideas  that  the  classical  writers  have  not 
had  the  forethought  to  anticipate. 

Some  teachers  escape  the  dangers  of  the  hand-to- 
mouth  illustration  by  more  or  less  unconsciously  ac- 
quiring a  stock  of  illustrations  that  they  stereotype, 
and  keep  in  hand  so  as  to  produce  them  on  appropriate 
occasions.  Great  weariness  often  results  for  the  pupils 
who  have  to  submit  to  the  same  illustration  without 
explanatory  comments  that  might  make  it  intelligible. 
As  soon  as  the  question  of  transitive  or  intransitive 
came  up,  a  certain  teacher  might  be  relied  upon  to 
make  the  following  remark,  and  no  other:  "The  cat 
cannot  sit  the  mat,  therefore  sit  is  intransitive."  Years 
afterwards  that  teacher's  pupils  spoke  with  bitterness 
of  that  intransitive  cat.  The  reproach  of  the  stereo- 
typed illustration  is  removed  when  it  can  be  shown  that 
it  is  a  real  touchstone  of  truth  that  may  be  applied  to  all 
cases  within  its  sphere.  For  instance,  there  is  a  peren- 
nial difficulty  among  young  students  of  French  about 
which  of  the  verbs  take  §tre  and  which  avoir  in  conju- 
gating their  past  tenses.  Some  text-books  deliberately 
give  lists  of  verbs  that  are  conjugated  with  avoir,  and 
no  attempt  is  made  to  lay  down  the  principle  that  may 
explain  this  peculiarity.  This  principle  seems  to  be 
that  where  the  action  of  the  verb  is  followed  by  a  corre- 
sponding state,  the  verb  &tre  is  to  be  used ;  in  all  other 


394    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

cases,  the  verb  avoir.  The  stereotyped  test  is  in  the 
form  of  the  question :  "  If  the  subject  has  done  so-and-so, 
is  it  so-and-so?  "  This  is  obviously  obscure,  so  a  parti- 
cular case  is  taken.  "If  the  subject  has  come,  is  it 
come?"  If  the  answer  is  yes,  then  etre  is  the  verb; 
if  no,  then  avoir.  It  may  be  simpler  to  adopt  the  form 
of  the  second  person:  "If  you  have  done  so-and-so,  are 
you  so-and-so?"  "If  you  have  eaten,  are  you  eaten?" 
No;  then  use  avoir.  But  whatever  the  form,  it  must 
enable  us  to  discriminate  between  those  cases  hi  which 
a  verb  sometimes  has  etre  and  sometimes  avoir.  Take 
the  verb  descendre,  with  the  subject  le  chef.  "If  le  chef 
has  descended,  is  he  descended?"  Yes;  therefore  etre. 
"If  le  chef  has  descended  the  dinner,  is  he  descended?" 
No ;  therefore  avoir.  Le  chef  a  descendu  le  diner. 

So  with  the  simpler  case  of  quotation  marks  hi  writ- 
ing a  dialogue.  The  pupil  may  be  given  the  stereo- 
typed question:  Did  the  speaker  open  his  mouth  and 
let  out  the  very  words  in  question?  If  the  answer  is 
yes,  then  quotation  marks  must  be  used.  With  duller 
pupils  some  teachers  adopt  the  grosser  device  of  making 
the  pupils  ask  themselves  whether  the  doubtful  words 
could  be  represented  within  the  bladders  of  words  that 
are  drawn  as  coming  out  of  the  mouths  of  persons  in  in- 
ferior comic  cartoons.  The  method  may  be  objection- 
able because  of  its  associations  with  trashy  literature, 
but  so  far  as  being  stereotyped  is  concerned,  no  harm  is 
done,  since  the  illustration  is  of  universal  application. 

In  almost  every  subject  the  hand-to-mouth  illustra- 
tor gets  into  trouble  by  demanding  from  his  pupils 
knowledge  that  is  not  yet  due  in  the  course  of  their 
study.  It  is  probably  unnecessary  to  labour  this 
point  here,  for  the  reader  who  has  taken  the  trouble  to 


DANGERS  OF  ILLUSTRATION  395 

follow  this  book  so  far  has  given  proof  that  he  has 
enough  interest  in  the  subject  of  method  to  prevent  his 
making  the  discreditable  bungles  that  not  infrequently 
mark  the  teaching  of  brilliant  scholars  who  rely  upon 
their  mere  knowledge  of  the  subject  to  carry  them 
through,  without  taking  the  trouble  necessary  to  make 
then*  teaching  efficient.  The  reader's  danger  may  in- 
deed be  quite  the  opposite.  Because  of  his  interest  in 
the  theoretical  aspect  of  his  work,  he  may  be  inclined  to 
over-elaborate  his  illustrations,  and  may  thus  fall  into 
certain  errors  that  are  likely  to  interfere  with  the  suc- 
cess of  his  teaching. 

To  begin  with,  there  is  the  danger  of  over-illustration. 
Some  teachers  seem  to  regard  it  as  an  established  prin- 
ciple that  every  point  that  arises  must  be  illustrated, 
whether  it  offer  any  difficulty  or  not.  What  is  per- 
fectly clear  already  needs  no  illustration  as  a  matter  of 
Exposition.  A  straightforward  statement  of  fact  deal- 
ing with  elements  that  come  well  within  the  pupil's 
range  should  not  be  illustrated,  so  long  as  the  teacher's 
purpose  at  the  time  is  only  to  get  the  pupil  to  under- 
stand. Indeed,  it  is  possible  that  by  illustrating  what 
requires  no  illustration  the  teacher  may  cause  needless 
difficulty  to  arise,  especially  in  the  minds  of  the  more 
eager  and  attentive  pupils.  Accustomed  to  attach 
a  meaning  to  all  the  teacher  says,  such  pupils  are  apt 
to  think  that  since  he  makes  so  much  of  the  point  he 
is  labouring,  there  must  be  something  in  it  which  they 
do  not  yet  perceive,  and  they  may  grope  about  for  a 
meaning  that  is  not  there. 

By  the  commonplace  teacher  the  temptation  to  over- 
illustration  is  easily  resisted.  His  danger  lies  in  quite  a 
different  direction.  But  there  is  a  very  real  risk  in  the 


396    EXPOSITION   AND   ILLUSTRATION   IN   TEACHING 

case  of  the  zealous  expositor.  No  limit  can  be  set  to  the 
possibilities  of  illustration,  once  the  lust  of  the  collector 
is  joined  to  the  enthusiasm  of  the  teacher.  Every  keen 
expositor  is  a  potential  grangerite. 

"  In  our  time  the  term  '  grangerite '  has  come  to  be  applied  to 
the  commentator  who  summons  illustration  to  his  aid  in  dealing 
with  a  book  already  printed.  That,  however,  does  not  cover  his 
art,  which  includes  everything  bearing  on  the  elucidation  of  the  text. 
I  use  the  word  'grangerising/  then,  as  a  term  for  the  general  art  of 
what  may  be  called  the  methodised  scrap-book  —  for  in  its  very 
method  it  differs  widely  from  the  olla-podrida  usually  known  by 
that  name."  l 

The  art,  named  after  the  Rev.  James  Granger,  who 
began  life  in  Dorset,  England,  in  1723,  is  full  of  attrac- 
tion, not  to  say  temptation,  for  the  industrious  and  in- 
genious teacher.  When  he  is  taking  a  class  through  one 
of  Shakespeare's  plays,  and  as  a  help  in  his  preparation 
cuts  up  two  cheap  copies  of  the  text  and  pastes  the  sepa- 
rate leaves  each  in  the  middle  of  one  of  the  pages  of  a 
large  manuscript  book,  so  that  he  may  fill  the  abundant 
margin  thus  supplied  with  notes  of  all  kinds  on  the  text, 
he  may  not  know  that  he  has  set  out  on  a  grangerising 
expedition.  He  cuts  out  some  critical  remarks  from 
newspapers  or  magazines  and  pastes  them  in  his  book. 
If  he  can  get  pictures,  he  naturally  includes  them  in  his 
collection.  By  and  by  it  is  clear  that  even  the  huge 
manuscript  page  is  insufficient,  and  a  new  book  is  neces- 
sary. He  is  not  likely  to  go  to  the  excess  that  drove 
Lefevre  to  grangerise  Voltaire  into  ninety  volumes, 
but  he  may  very  easily  be  carried  away  beyond  the 
bounds  of  prudence.  Kept  within  modest  limits,  a 
grangerised  copy  of  a  classic  to  be  studied  or  a  text- 

1  J.  M.  Bullock:  The  Art  of  Extra- Illustration  (1903)  p.  10. 


DANGERS  OF  ILLUSTRATION  397 

book  to  be  taught  is  a  valuable  possession,  both  for  the 
information  it  actually  contains  and  for  the  mastery  of 
the  subject  that  its  compilation  helps  to  secure.  But 
there  is  always  the  danger  of  the  collecting  interest 
getting  the  upper  hand,  and  the  book  becoming  an 
end  in  itself.  Instead  of  illustrating  the  original  text, 
it  dwarfs  that  text,  swamps  it,  drowns  it.  The  teacher 
must  never  forget  that  as  teacher  his  interest  lies  in  ex- 
pounding the  text  or  other  subject.  His  illustrations 
are  to  be  illustrations  of  the  original  subject.  The 
grangeriser  very  rapidly  gets  off  the  main  line  and  goes 
on  illustrating  illustrations,  till  the  real  subject  is  left 
far  behind.  What  the  teacher  must  avoid  is  well 
exemplified  in  Hill  Burton's  caricature  of  the  granger- 
ite's  methods  of  illustrating  the  familiar  lines:  — 

How  doth  the  little  busy  bee 

Improve  each  shining  hour, 
And  gather  honey  all  the  day 

From  every  opening  flower. 

"He  pictured  him  starting  with  the  poet,  Isaac  Watts.  This 
would  suggest  all  manner  of  bees,  —  Attic  and  other, — and  all  sorts  of 
beehives  would  be  appropriate,  to  be  followed  by  portraits  of  Huber 
and  other  bee-collectors,  and  views  of  Mount  Hybla  and  other 
honey  districts.  Burton  poured  good-humoured  contempt  on  the 
process  by  drawing  out  the  agony  of  subjects  to  be  illustrated; 
but  in  the  forty  years  that  have  elapsed  since  he  penned  the  Book 
Hunter,  the  subject  of  the  bee  has  been  extended  to  a  point  more 
elaborate  than  Burton  ever  contemplated.  To-day  the  exhaustive 
(and  exhausting)  grangerite  would  have  to  include,  for  example, 
a  portrait  of  Maeterlinck,  who  has  told  us  the  story  of  the  bee  in 
terms  of  the  most  charming  philosophy,  to  say  nothing  of  Lord 
Avebury's  many  works,  and  the  scientific  construction  of  the  bee- 
hive. Burton  then  went  on  to  say  that  the  grangerite  would  have 
to  remember  that  there  was  once  a  periodical  called  the  Bee,  edited 
by  Dr.  Anderson,  who  was  the  grandfather  of  Sir  James  Outram, 


398    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

whose  career  might  be  included.  Finally,  he  genially  suggested 
that,  when  the  illustrator  came  to  the  last  line,  'which  invites  him  to 
add  to  what  he  has  already  collected  a  representative  of  every 
opening  flower,  it  is  easy  indeed  to  see  that  he  had  a  rich  garden  of 
delights  before  him.' "  1 

A  French  psychologist,  writing  on  the  theory  of 
laughter,  admits  that  he  used  to  read  the  examples  of 
fallacious  reasoning  in  his  text-book  on  logic,  as  a  sort  of 
legitimate  jest-book.  George  Eliot  gives  us  a  delight- 
fully true  account  of  the  seductive  charms  of  the 
matter  supplied  in  the  illustrative  examples  hi  the 
Latin  grammar.  Maggie  Tulliver :  — 

"presently  made  up  her  mind  to  skip  the  rules  in  the  Syntax  — 
the  examples  became  so  absorbing.  These  mysterious  sentences 
snatched  from  an  unknown  context  —  like  strange  horns  of  beasts, 
and  leaves  of  unknown  plants,  brought  from  some  far-off  region  — 
gave  boundless  scope  for  her  imagination  —  the  fortunate  gentle- 
man whom  every  one  congratulated  because  he  had  a  son  'en- 
dowed with  such  a  disposition '  afforded  her  a  great  deal  of  pleasant 
conjecture;  and  she  was  quite  lost  in  the  'thick  grove  penetrable 
by  no  star.' " 2 

We  have  here  a  force  with  which  every  teacher  has 
to  reckon,  the  examples  always  have  been  and  always 
will  be  so  absorbing.  As  a  rule  they  are  not  hi  them- 
selves dangerously  interesting:  they  usually  obtain 
their  power  by  contrast  with  the  still  less  entertaining 
matter  of  the  text.  Even  the  publisher's  advertise- 
ments at  the  end  of  the  book  are  not  without  their 
attractions  as  a  relief  from  what  the  book  itself  con- 
tains. Making  all  allowance  for  this  unearned  incre- 
ment of  interest  that  attaches  to  examples,  we  find  that 

1  J.  M.  Bullock ;  The  Art  of  Extra  Illustration,  p.  19  (published  1903). 
The  original  passage  will  be  found  in  The  Book  Hunter,  Part  I,  "  Class- 
ification." l  M  ill  on  the  Floss,  Book  II,  Chap.  I. 


DANGERS  OF  ILLUSTRATION  399 

the  legitimate  attraction  of  the  examples  is  a  dangerous 
rival  to  the  teacher.  The  way  to  meet  the  difficulty  is 
not  to  make  all  the  examples  of  the  most  uninteresting 
character,  but  to  select  them,  as  far  as  possible,  from 
matter  that  has  already  exhausted  its  interest  in 
other  parts  of  school  work.  Let  the  teacher  consider 
the  wiles  of  the  clever  advertising  tailor  and  learn  of  him. 
In  a  certain  shop  in  Holborn,  London,  there  appeared 
a  little  while  ago  a  new  set  of  wax  heads  to  surmount  the 
dummies  that  displayed  the  ready-made  suits  hi  the 
window.  The  new  heads  were  exceedingly  well  made 
and  formed  a  very  agreeable  change  from  the  wooden 
knobs  that  had  formerly  finished  off  the  dummies. 
The  passers-by  were  greatly  interested,  and  gave  un- 
stinted admiration  to  the  type  of  head  adopted.  There 
was,  however,  one  fatal  defect  from  the  point  of  view 
of  the  critical  public.  The  whole  thirteen  heads  were 
of  exactly  the  same  pattern;  in  fact,  they  were  the  same 
head,  cast  in  the  same  mould,  coloured  with  the  same 
pigments  and  by  the  same  process,  supplied  with  the 
same  glass  eyes  and  the  same  curly  brown  hair.  On 
being  remonstrated  with,  the  tailor  admitted  that  his 
aim  was  not  entirely  disinterested.  The  heads  were 
specially  good  hi  order  to  attract  attention  to  his 
window.  They  were  made  exactly  alike  so  as  to  ex- 
haust very  rapidly  the  interest  of  the  onlooker,  who, 
disappointed  at  the  similarity,  sought  for  and  obtained 
the  necessary  variety  by  examining  the  different  kinds 
of  suits  of  clothes. 

In  the  case  of  teachers  who  use  as  examples  matter 
that  has  already  exhausted  its  interest  in  other  depart- 
ments of  school  work,  there  is  a  double  end  served  — 
old  matter  is  revised,  and  a  new  interest  is  created  in  it, 


400    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

which  new  interest  is  of  exactly  the  kind  the  teacher 
desires  to  arouse,  for  it  is  connected  with  the  work 
actually  in  hand.  The  pupil  is  interested  to  know  what 
the  teacher  is  going  to  do  with  this  familiar  old  fact 
that  is  being  presented.  The  whole  question  of  corre- 
lation is  involved  here.  Teachers  are  now  aware  of  the 
dangers  of  weariness  that  are  implicit  in  the  overzeal- 
ous  use  of  correlation.  But  our  present  consideration 
recognises  the  loss  of  interest  in  certain  parts  of  school 
work,  and  proposes  to  take  advantage  of  this  loss. 
Certain  matter  is  selected  because  it  has  lost  its  in- 
trinsic interest,  and  if,  in  the  process  of  teaching,  a  cer- 
tain amount  of  mediate  interest  is  developed,  that  is 
all  to  the  good. 

One  of  the  chief  dangers  of  the  use  of  illustration  is 
connected  with  this  problem  of  the  incidence  of  atten- 
tion. There  is  always  the  risk  that  the  illustration 
will  prove  more  attractive  than  the  illustrandum. 
The  attraction  to  which  Maggie  Tulliver  yielded  is  not 
confined  to  examples.  An  illustration  fails  when  it 
derails  the  interest  of  the  pupils  from  the  main  lines  of 
the  lesson.  In  the  case  of  certain  material  illustrations, 
such  as  models  or  pictures,  the  derailing  of  interest  is  so 
obvious  that  it  at  once  attracts  the  teacher's  attention, 
and  he  takes  means  to  recall  it  to  the  main  subject. 
This  is  comparatively  easily  done  if  he  has  the  sense  to 
allow  the  illustration  to  exhaust  most  of  its  primitive 
interest  before  he  proceeds  to  use  it  as  a  mere  illustra- 
tion. It  used  to  be  a  matter  of  professional  pride  with 
a  class  teacher  not  to  let  a  particularly  interesting  ob- 
ject be  seen  till  the  moment  came  at  which  it  had  to  be 
produced  for  illustration.  No  great  harm  resulted  if, 
when  it  was  introduced,  the  teacher  allowed  a  reason- 


DANGERS  OF  ILLUSTRATION  401 

able  time  for  the  pupils  to  gloat  over  it  before  he  began 
to  demand  their  attention  to  its  purely  illustrative 
aspect.  The  skilful  lecturer,  on  presenting  an  attrac- 
tive slide  on  the  screen,  follows  the  plan  recommended 
in  Chapter  VIII,1  and  allows  a  reasonable  time  for  the 
subsidence  of  that  gasp  of  appreciation  with  its  suc- 
ceeding murmur  of  whispers  that  welcomes  every  strik- 
ing picture.  When  he  does  begin  to  talk,  he  takes  care 
to  deal  with  comparatively  unimportant  matters  till 
the  edge  of  the  intrinsic  interest  of  the  slide  is  blunted. 
If  the  slide  is  really  important  as  an  illustration,  he 
may  introduce  it  at  an  early  stage  in  his  lecture  mainly 
to  rub  off  its  intrinsic  attraction.  At  its  first  appear- 
ance he  merely  calls  attention  to  facts  that  are  in  any 
case  attracting  the  attention  of  his  audience;  when, 
at  a  later  stage,  it  reappears,  he  is  able  to  direct  the 
attention  of  his  hearers  in  the  way  he  desires,  for  they 
are  now  able  to  concentrate  on  the  line  of  secondary 
interest  as  brought  out  in  the  illustrative  process. 

Too  frequently  the  derailing  of  interest  is  not  antici- 
pated by  the  teacher,  because  he  has  failed  to  consider 
the  immediately  preceding  content  of  the  minds  of  the 
pupils.  Any  reference  to  certain  of  the  more  urgent 
interests  of  the  pupils  may  be  an  excellent  way  of  getting 
up  a  secondary  interest  in  some  part  of  school  work. 
Mensuration  may  be  connected  with  the  football  field 
or  the  cricket  pitch,  hydrostatics  with  boating,  dynam- 
ics with  the  proceedings  in  the  gymnasium.  But  in 
all  such  cases  there  is  great  danger  of  derailing  the  in- 
terest from  the  school  subject.  No  doubt  it  may  be 
won  back  again,  but  in  a  case  of  class  instruction  it  is 
probable  that  the  temporary  aberration  has  caused  at 

'p.  208. 
2o 


402    EXPOSITION  AND  ILLUSTRATION   IN  TEACHING 

least  a  few  pupils  to  lose  some  important  link  that  they 
may  not  be  able  to  catch  up  during  the  course  of  the 
lesson. 

The  teacher  has  to  remember  that  every  illustration 
he  uses  must  run  the  gantlet  of  divergent  association  in 
the  mind  of  every  one  in  his  class.  He  can  never  be 
quite  sure  that  the  most  innocent  illustration  may  not 
derail  the  interest  of  some  of  his  pupils,  even  though 
he  takes  all  possible  precautions.  But  he  ought  at  least 
to  minimise  the  danger  by  doing  all  he  can  to  remove 
temptations.  For  example,  he  must  avoid  the  arith- 
metical challenge,  of  which  we  have  already  had  one  or 
two  examples.1  Certain  minds  are  so  constituted  that 
as  soon  as  two  terms  of  an  arithmetical  problem  are 
presented,  they  must  proceed  at  once  to  work  it  out. 
If  at  one  part  of  a  literature  lesson  the  master  mentions 
that  he  first  read  Lycidas  at  the  age  of  twelve,  and  at  a 
later  stage  that  it  is  now  a  quarter  of  a  century  since 
he  first  read  Lycidas,  a  large  number  of  his  pupils  will 
neglect  the  point  he  is  making  in  speaking  of  the  differ- 
ent effect  of  Lycidas  on  the  boy  and  on  the  man:  their 
attention  will  be  taken  up  in  calculating  the  exact  age 
of  the  master.  Young  people  are  particularly  open  to 
the  arithmetical  challenge  when  it  implies  a  certain 
amount  of  criticism  of  a  statement  made.  Though  it 
was  an  adult  mathematician  who  made  the  following 
arithmetical  criticism  of  Tennyson,  it  is  quite  in  the 
schoolboy  vein.  In  his  Vision  of  Sin  Tennyson  ven- 
tures the  statement:  — 

1  Pages  250,  309.  An  excellent  example  of  the  irritating  effect  of 
the  challenge  is  to  be  found  in  the  quotation  from  Mauclair  on  p.  337. 
The  hourly  change  and  the  "  twenty  times  "  call  for  explanatory  com- 
ment. 


DANGERS  OF  ILLUSTRATION  403 

"  Every  moment  dies  a  man, 
Every  moment  one  is  born." 

The  man  of  figures  at  once  accepted  the  challenge,  and 
pointed  out  that  if  this  were  true,  the  population  of  the 
world  would  necessarily  remain  stationary,  which,  of 
course,  was  contrary  to  recognised  facts.  He  suggested 
as  an  emendation  the  following:  — 

"Every  moment  dies  a  man, 
And  one  and  a  sixteenth  is  born."  * 

He  admitted  that  it  was  not  absolutely  accurate,  but  it 
was  at  least  approximately  correct.  It  is  because  this 
perverse  mathematician  takes  such  an  unreasonable 
view  that  the  story  forms  a  useful  illustration.  The 
pupil  ought  to  be  thinking  in  terms  of  poetry;  if  he 
persists  in  thinking  in  terms  of  number,  there  is  serious 
damage  done  to  the  lesson.  Even  when  no  reference  to 
number  is  involved  in  the  exposition,  certain  minds  are 
tempted  to  introduce  calculation.  One  of  the  students 
of  an  exceptionally  slow  lecturer  at  Oxford  confessed 
that,  in  the  inordinate  pauses  during  the  lecture,  he  ac- 
quired a  habit  of  calculating  what  each  pause  cost  him 
on  the  basis  of  so  much  for  a  course  of  twelve  lectures 
of  one  hour  each.  The  moral  for  the  teacher  is  that 
Satan's  employment  bureau  does  not  limit  itself  to 
manual  labor. 

Teachers  should  be  very  careful  in  their  use  of  the 
allusive  style.  Any  reference,  for  example,  to  a  person 
or  place  without  mentioning  the  name  will  often  set  up  a 
disturbance  that  takes  quite  a  long  time  to  settle  down. 
To  refer  to  Milton  in  a  lesson  merely  as  "the  author  of 
the  Defensio  Populi  Anglicani"  may  give  satisfaction 

1  Quoted  by  Paratus  in  the  British  Weekly,  June  3,  1909. 


404    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

to  a  certain  number  of  pupils  who  happen  to  know  who 
is  meant.  But  to  certain  others  the  reference  will  prove 
a  stumbling-block,  for  they  will  go  on  wondering  who  it 
can  be,  when  they  should  be  following  the  work  of  the 
class.  In  this  particular  case  the  average  boy  would 
probably  not  trouble  much,  for  the  reference  is  not  in 
itself  interesting  to  him.  But  let  the  teacher  use  some 
superlative  descriptive  reference,  and  dissipation  of 
attention  will  necessarily  follow.  "The  worst  king 
who  ever  ruled  England,"  "the  author  of  the  longest 
poem  in  the  English  language,"  are  references  that  will 
disturb  any  intelligent  class.  It  goes  without  saying 
that  it  is  a  laudable  thing  to  be  interested  in  discover- 
ing the  actual  persons  referred  to  in  such  statements. 
The  trouble  is  that  the  interest  is  roused  at  the  wrong 
time.  We  are  so  fond  of  rousing  interest  that  we  are 
apt  to  forget  that  it  is  as  necessary  to  allay  interest 
as  to  excite  it.  In  order  that  the  interest  of  the  pupils 
in  the  main  subject  of  the  lesson  may  be  maintained, 
all  subordinate  interests  must  be  ruthlessly  dissipated. 
The  way  to  kill  an  interest  is  to  satisfy  it.  Nothing 
must  be  left  for  the  imagination  to  work  upon.  Every- 
thing must  be  represented  with  pikestaff  directness, 
and  the  mind  will  seek  interest  elsewhere. 

While  writing  the  above  paragraph  I  have  furnished 
for  myself  an  unexpected  and  involuntary  illustration 
of  my  theme.  No  sooner  had  I  written  the  words, 
"the  author  of  the  longest  poem  in  the  English  language," 
than  I  began  to  feel  uncomfortable.  I  realised  that  I 
did  not  know  who  he  was,  and  I  began  to  wonder  who 
he  could  possibly  be.  Milton  wandered  through  my 
mind,  and  distracted  my  attention  from  the  main  sub- 
ject of  the  paragraph.  I  had  an  uneasy  feeling  that, 


DANGERS  OF  ILLUSTRATION  405 

though  the  Paradise  Lost  was  long,  it  was  far  from  being 
the  longest  poem  in  the  English  language.  I  had  a 
vague  memory  of  having  heard  the  phrase  "the  longest 
poem  in  the  English  language"  applied  to  Drayton's 
Polyolbion.  But  there  came  to  me  the  disquieting  im- 
pression that  I  had  somewhere  read  that  one  of  the  in- 
dustrious early  settlers  in  New  England  had  outstripped 
Drayton.  Could  it  be  Michael  Wigglesworth?  Next  I 
comforted  myself  with  the  reflection  that  all  I  had  to  do 
was  to  turn  to  some  standard  book  on  the  subject  of  lit- 
erature, and  get  the  matter  settled;  so  I  was  able  to  dis- 
miss temporarily  the  troublesome  interest  in  favour  of 
the  general  interest,  which  was,  in  any  case,  the  stronger. 
Had  I  been  a  careless  pupil  in  a  class  with  a  sporting 
interest  in  superlatives,  and  little  interest  hi  what  was 
going  on  at  the  tune,  it  is  probable  that  I  should  have 
continued  to  worry  about  that  longest  poem  instead  of 
turning  to  the  main  subject.1 

As  a  test  of  the  truth  of  the  view  here  adopted,  let  the 
reader  try  to  remember  whether  his  attention  was  not  a 
little  dissipated,  and  if,  indeed,  he  was  not  somewhat 
annoyed  by  the  unfinished  sentence,  "The  most  op- 
timistic writer  on  Education  is  .  .  .,"  introduced2  in 
Chapter  I  to  illustrate  the  mind's  tendency  to  anticipate 
what  is  coming.  Since  the  hiatus  has  served  its  pur- 
pose, the  reader  is  now  entitled  to  the  tardy  explana- 

1  On  referring  to  text-books,  I  found  no  help  in  settling  the  question, 
so  I  fell  back  upon  an  examination  of  some  of  the  poems  that  might 
claim  first  rank.     Paradise  Lost  reaches  the  modest  total  of  a  trifle 
over  10,500  lines.     The  Polyolbion  attains  to  nearly   16,000.     The 
Ring  and  the  Book  swells  out  to  21,133  lines.     But  the  limit  seems 
to  be  reached  in  Festus,  a  Poem,  by  Philip  James  Bailey,  which,  in 
its  reorganised  form  (Fiftieth  Anniversary  Edition,  1893),  reaches  a 
total  that  on  a  rough  calculation  amounts  to  40,800  lines. 

2  See  p.  15. 


406    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

tion  that  the  writer  referred  to  is  Helvetius,  who  boldly 
proclaims  "  L'education  peut  tout." 

Under  certain  conditions  the  allusive  style  may  be 
excellent  in  print,  but  when  used  in  lecturing  or  teaching, 
it  ought  to  be  limited  to  the  most  obvious  allusions, 
allusions  that  are  well  within  the  range  of  the  less 
informed  of  the  class  or  audience,  so  that  the  main 
effect  of  the  allusion  will  be  to  rouse  that  feeling  of  sat- 
isfaction that  accompanies  the  recognition  of  an  old 
friend  under  new  circumstances.  A  typical  example 
of  the  sort  of  thing  that  may  perhaps  be  permitted  in  a 
book,  but  that  must  be  excluded  from  oral  teaching,  is 
to  be  found  in  the  extract  from  Madame  de  Coulevain 
in  Chapter  XI  of  this  book.1  There  we  find  allusions  to 
"a  king,"  and  to  "two  of  our  great  newspapers,  one  of 
our  best  reviews."  At  this  point  Madame  de  Coule- 
vain's  reader  puts  his  finger  between  the  leaves  and 
leans  back,  wondering  who  that  king  and  what  those 
publications  can  be.  Unless  from  the  point  of  view 
of  piquancy,  the  allusions  are  a  mistake  in  exposition. 
If  there  were  any  indication  of  how  the  missing  names 
could  be  discovered  by  the  reader  for  himself,  there 
might  be  some  justification  for  the  mystification,  since 
it  would  rouse  him  to  take  a  fair  share  of  the  work. 
But  as  they  stand,  they  only  aggravate  the  reader  by 
making  him  feel  his  ignorance  and  —  it  is  no  extenu- 
ating circumstance  to  add  —  Madame  de  Coulevain's 
superiority.  Apart  from  this  unprofitable  disturbance 
of  mind,  the  same  end  could  be  obtained  by  saying 
merely  that  a  king  could  be  as  bourgeois  as  the  tenant 
of  a  flat,  and  that  some  of  our  great  newspapers  and 
reviews  are  bourgeois.  In  a  lecture  or  lesson  the  hearer 

1  See  p.  294. 


DANGERS  OF  ILLUSTRATION  407 

would  not  only  be  irritated  by  the  unintelligible  allu- 
sion, he  would,  necessarily,  from  the  distraction  of  his 
attention,  lose  a  great  deal  of  what  immediately  fol- 
lows the  derailing  references.  If  the  authoress  means 
Louis  Philippe,  why  not  say  so?  The  names  of  the  two 
great  newspapers  and  the  review  would  be  much  more 
illuminating  than  the  piquant  riddle  she  has  set  us. 
No  doubt,  in  thus  making  our  references  specific  we 
kill  a  certain  amount  of  interest,  but  the  interest  killed 
is  of  the  unhealthy,  distracting  kind;  and  it  has  always 
to  be  remembered  that  we  are  mainly  concerned  here 
with  the  didactic  use  of  illustration. 

An  author  may  feel  that  it  is  worth  while  to  aggravate 
his  duller  readers  so  long  as  he  wins  the  admiration  of 
the  clever,  and  if  he  is  prepared  to  pay  the  price,  there 
is  nothing  more  to  be  said.  The  irritated  reader,  on  his 
part,  is  free  to  throw  aside  the  tantalising  book.  But 
when  it  comes  to  oral  exposition,  it  is  necessary  to  carry 
the  whole  of  one's  audience  with  one.  We  cannot,  of 
course,  as  Dr.  Johnson  pointed  out  with  some  asperity, 
supply  our  hearers  with  understanding,  but  we  are  not 
justified  in  distracting  what  understanding  they  pos- 
sess by  leading  it  into  blind  alleys. 

I  have  had  occasion  already  to  refer  to  the  teacher's 
overgrown  respect  for  accuracy.  In  certain  forms  of 
illustration  this  respect  leads  him  into  serious  difficulties, 
for  there  practically  emerge  two  kinds  of  accuracy, 
and  these  two  kinds  cannot  be  reconciled.  He  has  to 
make  a  drawing  of  the  earth  as  an  "oblate  spheroid." 
If  he  makes  an  accurate  drawing,  the  pupils  will  be  un- 
able to  notice  any  difference  between  his  drawing  and  an 
ordinary  circle,  but  if  he  flattens  the  polar  ends  suffi- 
ciently to  make  the  true  shape  apparent,  he  has  played 


408    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

havoc  with  the  other  kind  of  accuracy,  and  multiplied 
many  times  the  paltry  six-and-twenty  miles  by  which 
the  equatorial  diameter  exceeds  the  polar.  Sir  John 
Herschel  may  speak  bluntly  about  circles  representing 
the  orbits  of  the  planets,  but  knowing  that  the  orbits  are 
really  ellipses,  the  teacher  is  in  a  strait  between  two.  If 
he  draws  them  as  circles,  he  is  inaccurate  qualitatively, 
for  they  are  not  circles;  but  if  he  draws  them  elliptical 
enough  to  make  his  class  easily  perceive  that  they  are 
not  circles,  then  he  has  to  err  quantitatively.  For  they 
are  not  so  elliptical  as  all  that.  Clearly,  the  teacher 
must  be  allowed  sufficient  quantitative  exaggeration 
to  make  clear  his  qualitative  distinctions.  If  his  pupils 
are  at  a  stage  at  which  it  is  important  that  they  should 
know  that  the  earth  is  an  oblate  spheroid,  then  he  must 
be  permitted  so  to  represent  it  as  to  suggest  that  particu- 
lar form.  It  is  quite  a  different  matter  when  little 
children  are  sedulously  taught  that  the  earth  is  "nearly, 
but  not  quite,  a  perfect  globe."  This  is  the  same  lust 
for  accuracy  that  has  canonised  the  additional  two  feet 
in  the  height  of  Kinchin junga  —  "twenty-nine  thou- 
sand and  two  feet."  Naturally,  intelligent  pupils  will 
be  warned  when  necessary  exaggerations  are  made. 
They  will  be  told,  for  example,  that  though  the  earth's 
orbit  is  elliptical,  its  major  axis  is  not  quite  so  big  in 
proportion  to  the  minor  as  the  drawing  would  make  out. 
Another  very  real  danger  in  the  use  of  illustration  is  the 
tendency  to  carry  over  the  illustration  as  a  whole  with 
non-essential  as  well  as  essential  elements.  A  teacher 
wished  his  class  to  understand  that  for  a  particular  ex- 
periment he  was  describing  it  was  necessary  to  cut  out 
an  oblong  piece  from  the  middle  of  one  end  of  a  board. 
As  some  of  the  pupils  had  a  difficulty  in  understanding 


DANGERS  OF  ILLUSTRATION  409 

what  he  meant,  he  explained  that  the  bit  cut  out  was  to 
leave  a  hole  in  the  bottom  of  the  board,  so  that  when  it 
was  placed  on  end  there  would  be  an  opening  in  it  like 
the  entrance  to  a  dog's  kennel.  This  seemed  to  satisfy 
the  pupils,  but  at  a  later  stage,  when  they  had  to  make 
a  drawing  of  the  apparatus,  several  of  them  made  the 
board  appear  as  a  pentagon,  like  the  gable  end  of  a 
house.  They  had  carried  the  kennel  comparison  too 
far.  What  in  this  case  could  be  tested  by  the  sketches, 
would,  in  the  case  of  merely  verbal  description,  probably 
have  escaped  detection,  and  with  young  children,  in 
particular,  it  is  probable  that  many  of  our  illustrations 
are  carried  over  bodily  and  incorporated  in  connections 
in  which  certain  of  their  elements  are  quite  out  of  place.1 
The  teacher  must  be  continually  on  his  guard,  and  must 
try  to  anticipate  and  avoid  possible  misconceptions  of 
this  kind.  Nearly  always  he  will  find  that,  in  spite  of 
all  his  endeavours,  some  dull,  commonplace  child  has 
contrived  an  impossible  combination  that,  had  it  been 
deliberately  made,  would  be  regarded  as  very  ingenious. 
To  meet  such  contingencies  a  certain  amount  of  verbal 
pruning  is  necessary,  but  above  all  there  ought  to  be  a 
good  deal  of  intercourse  in  the  way  of  applying  illustra- 
tions. A  teacher  in  a  city  school,  in  giving  a  lesson  on 
the  Charge  of  the  Light  Brigade  at  Balaclava,  made 
a  sketch-plan  on  the  blackboard,  with  the  Russian  guns 
on  the  right  of  the  board  and  the  formation  of  hussars 
represented  by  two  vertical  lines  on  the  left.  The  class 
as  a  whole  seemed  to  understand  the  state  of  affairs  on 
the  field,  but  in  the  course  of  discussion  it  came  out 
that  some  of  the  boys  (the  average  age  of  the  class  was 
12+)  thought  a  mistake  had  been  made  in  the  position 

1  Cf.  the  Castle  misunderstanding,  p.  112. 


410    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

of  the  hussars.  As  they  were  represented,  the  boys 
maintained,  they  were  charging  either  north  or  south 
instead  of  eastwards,  as  they  ought  to  do  if  they  meant 
to  get  at  the  Russian  guns.  On  probing,  the  teacher 
discovered  that  the  double  line  had  misled  the  boys. 


There  was  a  cavalry  barracks  in  the  city,  and  when  the 
troops  passed  through  the  streets,  they  always  went  two 
abreast  because  of  the  traffic.  The  boys  had  got  it  into 
their  heads  that  this  two-abreast  mode  of  progression 
was  the  natural  one  for  cavalry,  and  that  therefore  they 
would  charge  in  this  order.  It  was  a  revelation  to  them 
that  the  charge  was  made  with  such  a  wide  front. 

Allied  to  this  error  of  carrying  over  non-essentials  is 
that  of  arousing  altogether  wrong  masses  of  ideas  through 
some  superficial  resemblance.  Beginners  in  landscape 
painting  are  warned  against  the  little  cottage  on  the 
hillside  with  its  two  tiny  windows,  one  on  each  side  of  the 


DANGERS  OF  ILLUSTRATION  411 

door,  and  the  little  doorstep,  with  the  resulting  resem- 
blance to  a  grotesque  human  face.  Not  infrequently 
young  people  see  a  ludicrous  aspect  of  some  matter  that 
to  the  adult  mind  appears  to  be  of  the  most  matter-of- 
fact  character.  "Speaking  of  babies,"  said  the  Sunday- 
school  superintendent,  "I  have  a  baby  in  my  eye  now." 
He  was  quite  serious,  and  did  not  at  first  understand 
what  the  youngsters  found  to  laugh  at  in  what  he  re- 
garded as  a  very  commonplace  statement.  Occasion- 
ally private  jokes  of  this  kind  interrupt  the  attention 
of  individual  pupils,  but  it  is  the  business  of  a  good 
teacher  to  anticipate  and  provide  against  any  such 
misapplication  of  ordinary  words,  so  far  as  such  mis- 
applications are  likely  to  affect  a  whole  class.  The 
teacher's  safety  here  depends  upon  his  knowledge  of 
the  pupil's  mental  content.  Unintentional  jokes  ha 
class  are  always  the  mark  either  of  ignorance  or  of  bad 
psychology. 

Illustrations  are  often  put  in  what  the  illustrator 
regards  as  a  striking  way,  and  yet  are  apt  to  mislead  the 
pupils  because  of  their  very  vividness.  I  have  heard  a 
teacher,  in  seeking  to  give  his  class  an  adequate  idea  of  the 
size  of  London,  make  the  statement  that  if  all  the  houses 
in  that  city  were  placed  end  to  end,  they  would  reach 
right  round  the  earth,  following  the  equator.  In  dealing 
with  the  class  afterwards,  I  found  that  the  general 
impression  produced  was  complicated  by  an  incongru- 
ous picture  in  the  pupils'  minds  of  an  interminable 
street,  with  only  one  side  to  it.  Quite  a  number  of  the 
pupils  had  the  literal  objection  that  most  of  the  houses 
would  be  flooded,  as  the  equator  was  for  most  of  the 
time  over  the  ocean.  On  asking  the  teacher  how  he 
got  his  data  for  the  measurement,  he  frankly  confessed 


412    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

that  he  had  no  data,  but  "thought  it  would  be  a  very 
effective  way  of  bringing  home  to  the  class  the  enor- 
mous extent  of  the  city."  He  further  wanted  to  know, 
"morals  apart,"  what  objection  I  had  to  the  illustra- 
tion. The  objection  is  indicated  in  the  incongruity 
brought  out  above,  and  also  in  the  mistaken  notion 
that  in  some  way  or  other  the  imagination  of  the  pupils 
is  aided  by  the  picture  of  this  straggling  street.  After 
all,  the  figure  suggested  great  extent,  but  nothing 
more.  It  carried  the  pupils  far  past  the  Threshold  of 
Stun. 

A  companion  picture  to  that  supplied  by  this  ingen- 
ious teacher  is  to  be  found  in  a  text-book  of  geography 
that  seeks  to  emphasise  the  progress  of  London  in  this 
way:  "A  house  rises  out  of  the  ground  every  hour  of  the 
day;  a  village  of  more  than  three  hundred  persons  is 
added  to  its  population  every  day."  l  This  has  ob- 
viously no  pictorial  value.  We  certainly  do  not  want 
to  figure  forth  the  hourly  emergence  of  a  completed 
house,  and  the  very  name  of  a  village  suggests  some- 
thing antipathetic  to  the  city  spirit.  The  mere  state- 
ment of  a  daily  increase  of  three  hundred  inhabitants 
is  sufficiently  clear  without  the  obscuring  figure.  So 
far  as  the  figure  is  pictorial,  it  is  inaccurate.  The  popu- 
lation does  not  increase  in  that  good-naturedly  uniform 
way.  The  figure  interferes  with  the  pupil's  chance  of 
clearly  understanding  the  theory  of  averages.  As  a 
matter  of  fact,  in  actual  experience  I  have  found 
that  quite  a  large  percentage  of  those  to  whom  I  have 
presented  this  illustration  have  at  once  accepted  the 
arithmetical  challenge  and  multiplied  300  by  365  to  get 
the  annual  increase,  and  have  maintained  that  the 

1  Meiklejohn  :  The  British  Empire,  p.  49. 


DANGERS  OF  ILLUSTRATION  413 

resulting  109,500  was  much  more  stimulating  than  the 
daily  village. 

There  may  be  cases  at  a  very  low  stage  of  intelligence 
when  a  crude  illustration  of  a  pictorial  kind  may  enable 
a  person  to  understand  in  a  very  inaccurate  and  in- 
complete way  something  that  he  cannot  otherwise 
understand  at  all.  To  this  class  belongs  the  ingenious 
figure  by  which  one  Italian  rustic  conveyed  to  another, 
who  was  puzzled  by  the  telegraph,  some  conception  of 
the  possibility  of  what  a  man  does  at  one  end  of  a  wire 
producing  an  effect  at  the  other.  Starting  from  the 
well-known  fact  that  if  you  pinch  your  dog's  tail  the 
bark  issues  from  the  other  end,  the  expositor  invited  his 
friend  to  imagine  that  his  dog  grew  long  enough  to  reach 
from  Milan  to  Rome,  having  its  tail  end  in  Milan  and 
its  head  end  in  Rome.  It  then  became  clear  that,  if 
you  pinch  the  tail  in  Milan,  the  bark  will  take  place  hi 
Rome.1 

In  dealing  with  Exemplification,  it  is  obvious  that 
the  elements  found  in  the  illustration  must  be  cognate 
with  those  found  in  the  illustrandum.  But  when  we 
are  dealing  with  analogical  illustration,  it  is  desirable 
that  the  material  should  be  different  in  the  two  cases. 
This  is  manifestly  true  in  the  aesthetic  use,  but  it  also 
holds  in  didactic  work.  It  is  a  mistake  to  use  exactly 
the  same  sort  of  material  in  the  illustration  as  is  found 
in  the  illustrandum,  unless  the  very  fact  of  this  com- 
munity of  material  is  to  be  utilised  as  a  part  of  the  illus- 
trative process.  If  you  turn  to  Chapter  V,  p.  133,  you 

1  The  story  ends  here,  but  we  can  imagine  the  triumph  of  the  dull 
one  in  pointing  out  the  impossibility  of  getting  through  a  message 
from  Rome  to  Milan,  and  the  intelligent  one's  satisfaction  in  suggesting 
an  additional  but  inverted  dog. 


414    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

will  find  a  case  in  point.  There  I  wished  to  illustrate 
the  weakness  of  the  negative  not  as  against  the  positive 
suggestion  represented  by  a  noun  or  a  verb.  Turning 
my  thoughts  to  the  Lathi  grammar  for  an  example  of 
two  terms  often  confused  with  each  other,  I  found  the 
words  non  and  ne  had  arisen  in  my  mind.  They  were 
probably  suggested  by  the  fact  that  I  was  dealing  with 
the  subject  of  negatives  at  the  tune.  In  themselves 
they  form  quite  a  good  illustration,  but  as  soon  as  I 
reread  the  passage  I  saw  that  there  was  a  certain  con- 
fusion likely  to  arise  in  the  reader's  mind.  He  might 
very  naturally  think  that  the  Latin  negatives  as  nega- 
tives had  something  to  do  with  the  general  subject  of 
the  paragraph.  In  any  other  book  I  would  at  once 
have  changed  the  illustration  to  some  other  two  terms, 
—  perhaps  scire  and  cognoscere,  —  but  an  example  of  an 
actual  blunder  in  illustration  in  the  very  act  of  treating 
of  illustration  was  too  useful  to  be  thrown  aside,  so  I 
let  the  blunder  stand.  Further,  no  reference  was  made 
to  it  in  the  earlier  chapter,  in  order  to  give  the  reader 
an  opportunity  of  testing  at  a  later  stage  whether  he 
could  remember  any  slight  confusion  having  arisen  hi 
his  mind  at  the  tune. 

A  final  danger  of  the  use  of  certain  forms  of  illustra- 
tion is  said  to  be  the  tendency  it  has  to  make  the  pupils 
dependent  on  illustrations  for  then*  actual  thinking. 
They  become  incapable,  it  is  said,  of  doing  any  thinking 
at  all  unless  suitable  illustrations  are  supplied.  They 
never  trouble  to  deal  with  a  generalisation  till  it  is 
followed  by  illustrations.  But  it  is  surely  undesirable 
that  pupils  should  be  encouraged  to  accept  generalisa- 
tions without  examples,  and  sufficient  cautions  have 
been  already  given  against  allowing  the  pupil  to  adopt 


DANGERS  OF  ILLUSTRATION  415 

a  purely  passive  attitude  in  respect  of  illustrations. 
The  active  reaction  of  the  pupil  being  secured,  he  will, 
of  necessity,  provide  certain  illustrations  of  his  own. 
Indeed,  the  supplying  of  fresh  illustrations  by  the  pupil 
is  one  of  the  best  ways  of  his  securing  a  mastery  over 
the  illustrandum. 


CHAPTER  XVII 

THE  TORPEDO  SHOCK 

IN  Plato  we  find  Meno,  after  being  treated  on  the 
aggravating  Socratic  method,  driven  to  complain:  — 

"  O  Socrates,  I  used  to  be  told  before  I  knew  you  that  you  were 
always  doubting  yourself  and  making  others  doubt ;  and  now  you 
are  casting  your  spells  over  me,  and  I  am  simply  getting  bewitched 
and  enchanted,  and  am  at  my  wits'  end.  And  if  I  may  venture  to 
make  a  jest  upon  you,  you  seem  to  me  both  in  your  appearance  and 
in  your  power  over  others  to  be  very  like  the  flat  torpedo  fish,  who 
torpifies  those  who  come  near  him  and  touch  him,  as  you  have  now 
torpified  me,  I  think.  For  my  soul  and  my  tongue  are  really  torpid, 
and  I  do  not  know  how  to  answer  you."  l 

This  is  a  passage  that  touches  closely  all  of  us  who 
concern  ourselves  with  the  theory  of  method  in  teaching; 
for  there  is  a  certain  danger  that  in  setting  forth  more 
or  less  elaborate  theories  we  may  induce  a  mild  form 
of  intellectual  paralysis  in  the  teachers  whom  we  seek 
to  influence.  After  learning  the  numberless  possibili- 
ties of  going  wrong,  and  the  small  chance  of  hitting  upon 
the  absolutely  right  way  to  deal  with  any  particular 
case  that  arises,  the  student  of  method  may  not  un- 
naturally become  discouraged.  There  are  not  lacking 
people  who  say  that  to  study  method  is  to  acquire  know- 
ledge that  is  not  only  of  little  use,  but  is  positively 
noxious.  Their  attitude  reminds  me  of  the  indignant 
protest  of  an  old  college  acquaintance  of  mine,  a  medical 

1  Meno,  80,  A.  Jowett's  English. 
416 


THE  TORPEDO  SHOCK  417 

student,  who  had  just  come  down  in  his  anatomy: 
"What's  the  sense  in  knowing  every  miserable  nerve 
in  the  neck  ?  There's  Launceston  knows  'em  all,  and  is 
so  nervous  he's  afraid  to  put  in  his  knife  in  case  he 
severs  some  of  'em.  I  don't  know  'em,  so  I've  confi- 
dence. I  stick  in  my  knife,  and  there  you  are."  It 
need  hardly  be  said  that  Launceston  was  nervous  by 
temperament,  and  not  because  he  was  the  medallist  in 
anatomy.  Real,  positive  knowledge  gives  power  and 
confidence.  The  man  with  wide  and  accurate  know- 
ledge is  not  afraid  to  give  an  opinion  and  act  upon  it, 
though  he  has  no  monopoly  of  this  courage.  Neverthe- 
less, there  is  a  certain  danger  attending  the  close  study 
of  method.  All  the  positive  principles  mastered  are  of 
direct  service  in  practical  work,  and  your  hurriedly 
trained  person,  with  little  theory  and  a  great  deal  of 
practice,  is  only  too  willing  to  lay  down  the  law  and 
put  it  into  immediate  operation.  But  the  thoughtful 
student  who  looks  all  round  the  subject,  and  notes  this 
defect  and  the  other,  even  in  methods  that  are  on  the 
whole  excellent,  has  not  the  certainty  of  his  less  critical 
fellow.  The  man  of  criticism  is  always  less  confident 
than  the  man  of  action.  It  is  important,  therefore,  that 
critical  study  should  be  accompanied  by  the  corrective 
of  vigorous  practice.  The  work  of  the  study  must  be 
brought  to  fruition  in  the  class  room.  But  this  is  not 
quite  the  same  thing  as  to  say  that  the  student  is  to 
carry  his  theories  with  him  and  painfully  apply  them 
by  a  conscious  effort  in  front  of  his  class.  I  have  seen 
a  man  fishing  in  a  pond  in  Buckinghamshire,  with  a  book 
by  his  side  with  the  alluring  title  "How  to  Angle." 
To  this  he  referred  when  matters  became  critical  —  but 
he  caught  no  fish. 

2E 


418    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

In  the  stress  and  strain  of  the  class  room  the  teacher 
must  be  independent  of  the  book  of  method.  I  have  no 
doubt  that  a  great  deal  may  be  learnt  about  angling  in 
the  study,  but  the  riverside  is  not  the  place  to  continue 
the  study  as  study.  This  is  by  no  means  an  admission 
that  those  depressing  critics  are  right  who  maintain 
that  in  education  theory  and  practice  cannot  be  harmo- 
nised. ' '  Theory  is  all  very  well  in  the  study,  but  when  a 
man  gets  before  a  class  — "  This  sort  of  sentence  is 
usually  left  unfinished,  which  is  a  pity.  It  would  be 
pleasant  to  have  a  frank  statement  of  the  acceptance 
of  rule  of  thumb. 

As  a  matter  of  experience  there  is  no  difficulty  in 
combining  theory  and  practice,  but  the  combination 
cannot  be  made  in  the  mechanical  way  that  lends 
itself  to  easy  registration  in  an  educational  book.  The 
matter  was  put  epigrammatically,  but  with  a  different 
kind  of  truth  than  that  the  epigrammatist  intended  in 
the  complaint:  "So  far  as  I  can  gather,  students  of 
method  learn  laboriously  certain  principles  that  they 
forget  the  moment  they  are  face  to  face  with  a  class." 
For  the  outside  observer  this  is  a  sufficiently  accurate 
description  of  what  takes  place;  but  the  inner  meaning 
of  the  change  of  attitude  is  apt  to  be  overlooked  by 
the  casual  person.  A  better  description  of  the  same 
phenomenon  would  be  to  say  that  the  moment  the 
student  of  method  gets  before  a  class  he  loses  conscious- 
ness of  the  theoretical  principles  he  has  been  studying. 
It  does  not  follow  that  those  principles  have  lost  their 
influence.  It  is  all  a  matter  of  the  incidence  of  con- 
sciousness. Too  frequently  it  is  true  that  theoretical 
considerations  do  obtrude  themselves  on  the  considera- 
tion of  the  inexperienced  teacher  when  he  should  be 


THE  TORPEDO  SHOCK  419 

giving  himself  up  entirely  to  practice.  This  means  that 
he  has  not  mastered  his  principles,  and  therefore  is 
unable  to  forget  them  hi  the  moment  of  application.  A 
man  who  has  been  trained  by  a  proper  combination  of 
theory  and  application  of  theory  gradually  acquires  the 
right  to  forget  all  about  theory  when  he  is  engaged  in 
practice.  His  theory  has  become  a  part  of  himself, 
and  affects  his  activities  even  when  he  is  not  at  all 
thinking  of  theory.  The  facts  of  theory  have  become 
the  faculty  of  practice. 

One  of  my  students  told  me  the  other  day  that  she  did 
not  believe  she  could  begin  a  sentence  with  the  word 
And,  even  if  she  were  writing  in  her  sleep,  so  thoroughly 
had  this  part  of  the  teaching  of  the  theory  of  compo- 
sition been  assimilated.  She  remembered  that  the 
teacher  had  given  her  a  great  many  reasons  why  no 
sentence  should  ever  begin  with  the  word,  —  reasons 
that  many  modern  authors  would  dismiss  with  scant 
ceremony, — but  these  she  could  rather  guess  at  than 
remember;  the  important  point  is  that  they  had  consoli- 
dated themselves  into  an  inveterate  rejection  of  this 
conjunction  as  the  first  word  in  a  sentence. 

This  little  chapter  is  added  mainly  to  reassure  readers 
who  may  be  disturbed  by  the  criticisms  that  have  been 
made  of  certain  illustrations  that  are  not  in  themselves 
very  bad,  but  are  not  so  good  as  they  might  be.  The 
reader  in  his  modesty  may  protest  that  he  will  be  only 
too  glad  if  in  the  rough-and-tumble  of  strenuous  teaching 
he  can  evolve  such  good  illustrations  as  are  held  up  as 
warnings  in  these  pages,  and  may  feel  a  little  uneasy 
lest  in  the  moment  of  action  some  memory  of  criticism 
may  arise  and  torpify  him.  From  this  point  of  view 
illustrations  must  be  regarded  as  of  two  distinct  kinds: 


420    EXPOSITION  AND  ILLUSTRATION  IN  TEACHING 

those  that  are  prepared  for  before  the  lesson,  and  those 
that  are  summoned  on  the  spur  of  the  moment  to  clear 
up  more  or  less  unexpected  points  as  they  arise.  For 
confused  or  careless  illustrations  of  the  first  class  there  is 
never  any  excuse;  but  for  those  of  the  second  class  there 
must  be  great  allowance  made.  Still,  the  more  practice 
the  teacher  has  in  preparing  good  illustrations  before  the 
lesson,  the  greater  his  power  of  improvising  illustrations 
that  do  not  break  any  of  the  principles  to  which  he  has 
given  his  assent.  In  teaching  we  must  let  ourselves  go : 
the  practical  interests  of  the  moment  must  dominate 
everything.  But,  after  all,  teaching  is  not  a  mechanical 
process.  We  do  not  need  to  leave  our  minds  at  the  door 
of  the  class  room  as  the  Mohammedan  leaves  his  shoes 
on  the  mat  before  entering  the  mosque.  A  trained 
rhetorician  addressing  a  public  assembly  does  not  think 
of  the  laws  of  rhetoric  as  he  makes  his  appeal.  But  he 
does  apply  them.  The  teacher  must  be  able  to  think 
on  his  feet;  must  be  capable  of  changing  an  illustration 
hi  the  process  of  making  it;  and  must  all  the  while  de- 
pend upon  the  paid-up  capital  of  his  theorising  to  keep 
him  straight.  No  doubt  he  will  often  make  mistakes, 
and  will  wonder  afterwards  how,  knowing  what  he  did, 
he  could  have  made  this  blunder  and  that.  But  as  the 
result  of  his  studies  he  knows  that,  in  the  main,  he  is 
right.  Every  blunder  he  makes  gives  him  something 
to  consider  after  the  lesson.  But  it  is  to  be  used  in  warn- 
ing him  against  repetitions  of  this  error  and  its  like  and 
in  strengthening  his  grip  of  the  positive  principles  of  his 
art,  not  in  discouraging  him,  and  sapping  his  confidence 
in  himself. 


INDEX 


Abstract,  place  of  the,  in  illustration, 

248;     interaction    with    concrete, 

280-281. 

Abstraction  in  models,  320,  322. 
Accuracy,  excess  of,  408. 
Advertising,  22  note,  350,  399. 
Mneid,  105,  138. 

^Esthetic  illustration,  21-22,  242,  369. 
Alexander,  Professor  S.,  128,  386. 
Algebra,  184. 
Allen,  Grant,  192. 
Allen,  Professor  J.  W.,  6. 
Alpha  Centauri,  306. 
Alphabetical  index,  253,  273. 
Analogy,  73,  90,  91 ;  mathematical, 

230 ;   spreading  of,  232. 
Analysis,  the  lust  of,  64 ;  of  sentences, 

201. 

Analytic  step,  147. 
Anderson,  Robert,  310,  379. 
Anticipation,    in    listening,    15;     by 

contraries,    16;     in    presentation, 

207  note. 

Anticipatory  illustration,  31,  32,  33. 
Apperception,  37;  masses,  71,  74. 
Application  step,  151—152. 
Approaches,  kinds  of,  226. 
Archimedes,  118. 
Areas,   feebleness  in  estimating,  357 

ff.;  of  United  States,  364 ;  cultiva- 
tion of  sense  of,  376. 
Aristotle,  230,  234,  240. 
Arithmetic,  176,  281. 
Arithmetical  challenge,  250,  309,  332 ; 

(by  implication),  402,  412. 
Armstrong,  Professor  H.  E.,  34. 
Arnold,  Dr.,  272. 
Arrest,  71-74,  234. 
Arrows,  in  diagrams,  386,  388. 
Artists',    difficulties    in    illustration, 

345-347;   carelessness,  342. 
Ascham,  Roger,  101,  257. 
Association,  systematic,  70,  72,  73; 

step,  148;  divergent,  292,  402. 


Assumptions  underlying  theory  of 
Formal  Steps,  145  ff. 

Attendant  circumstances,  293. 

Attention,  119;  rhythm  of,  157;  in- 
tensity of,  158;  incidence  of,  400; 
fixed  by  lines,  385. 

Audiles,  188. 

Author  and  artist,  relations  of,  in 
illustration,  342  ff . 

Automatic,  view  of  mind,  117-118; 
level,  163. 

Auto-suggestion,  129  ff. 

Awful  example,  220,  254. 

Backgrounds:  emotional,  92;  har- 
monising of,  95;  elements  of,  97; 
kinds  of:  fixed,  100;  unstable, 
102;  mobile,  103;  to  sermons, 
103;  to  lectures,  104;  temporary, 
107;  normal,  122;  preferential, 
123;  relation  to  suggestion,  126. 

Bacon,  23,  25. 

Bailey,  Philip  James,  405  note. 

Bain,  Professor  A.,  116  note. 

Balaclava  illustration,  409. 

Baldwin,  Professor  Mark,  127. 

Ball,  Sir  Robert,  307-308. 

Barnett,  P.  A.,  389. 

Bates,  Charles  Austin,  22  note. 

Beginning,  62,  105;  degrees  of,  179; 
problem  of,  178,  179;  determines 
order  of  presentation,  182 ;  condi- 
tions determining,  195;  thinking 
a,  278. 

Bell,  Sir  Charles,  140. 

Bennett  and  Bristol,  155  note. 

Beranger,  137. 

Binet  and  Henri,  384  note. 

Biology,  teaching  of,  323. 

Bipolar  processes  and  terms,  10. 

Blast-furnace  temperature,  301. 

Bosanquet,  Professor,  211. 

Botany,  teaching  of,  322. 

Bourgeoisisme,  294-295. 


421 


422 


INDEX 


Brackenbury,  L.,  189. 

Bradley,  F.  H.,  39,  116  note,  230 
note. 

Brain-action,  theories  of,  88-90. 

British  Isles  and  British  Empire, 
position,  327;  trade  and  popula- 
tion, 369 ;  372. 

Browne,  Sir  Thomas,  150. 

Bruce,  Robert  the,  96,  97. 

Bullock,  J.  M.,  396,  398. 

Burns,  291. 

Burton,  J.  Hill,  397. 

Csfisar,  154,  321,  322. 

Calder,  Mr.  John,  387. 

Campe,  173  note,  175  note. 

Caran  d'Ache,  381. 

Castellar,  Maurice,  140. 

Catalogue  elaboration,  287. 

Challenge,  arithmetical,  253,  309, 
337;  (by  implication),  402-403; 
412. 

Chapman,  18. 

Chesterfield,  250. 

Chesterton,  G.  K.,  8  note. 

Chromatists,  336. 

Circle,  in  diagrams,  374-376;  of 
thought,  179. 

Classification,  59-60. 

Clearly  imaged  ends,  176. 

Collier,  Hon.  John,  91,  199  note. 

Colour,  idea  of,  48 ;  in  diagram,  368 ; 
of  shadows,  76,  246;  affected  by 
canvas,  91. 

Columns  in  diagrams,  371. 

Combination,  false,  209. 

Complex,  64,  98,  102,  198,  287; 
ready-made,  108. 

Complication,  73-74. 

Composition,  exercises  in,  299. 

Compromise  in  education,  99. 

Concentration  beat,  159. 

Concept,  55  ff . 

Concrete,  interpretation  of,  245;  to 
abstract,  280. 

Confrontation,  79,  80,  81. 

Consciousness,  individual  and  general, 
38;  field  of,  67-68,  84;  distribu- 
tion of,  68 ;  stream  of,  68. 

Contenement,  202. 

Continents,  area  of,  illustrated,  359  ff . 

Continuum,  69,  97. 

Contorniates,  218. 


Contradiction  and  reconciliation,  78. 

Contrariant  characters,  132. 

Co-ordinate  planes,  333. 

Correlation,  excess  of,  27 ;   400. 

Correspondence  between  inner  and 
outer  worlds,  54. 

Coteries,  95. 

Coulevain,  Madame  de,  294-295,  407. 

Countries  of  Europe,  size  of,  illus- 
trated, 360-361. 

Cramming,  213. 

Cross  purposes,  94. 

Cruikshank,  349. 

Cubic  content,  377. 

Cubic  mile,  311  ff. 

Deductive  methods  of  teaching,  156- 
157. 

Definition,  place  of,  58;  concrete 
form  of,  247 ;  wider  sense  of,  294. 

De  Ganno,  Charles,  147  note. 

Delaware,  area,  361. 

Demonstrate,  meaning  of,  3. 

De  Quincey,  6,  11,  242,  243,  244. 

Diagram,  undrawn,  245;  distin- 
guished from  picture,  348;  of  the 
seasons,  327-328;  place  of,  in 
teaching,  355;  danger  of  pictorial 
element  in,  355  ff . ;  two  kinds  of, 
367;  colour  in,  368;  "of  illustra- 
tion," 367,  390. 

Diagrammatic,  352. 

Dialectic,  12  note;  Socratic,  276. 

Dickens,  Charles,  8  note,  290-291; 
350. 

Diesterweg,  173  note. 

Diffusion  beat,  159. 

"Directions,"  208. 

Discovery  distinguished  from  apper- 
ception, 236. 

Docendum,  6  note,  11,  26. 

Doyle,  Sir  A.  Conan,  285-286. 

Drayton,  405. 

Drummond,  Professor  Henry,  230. 

Dunnottar  Castle  as  misleading  type, 
113. 

Dynamic  view  of  concept  and  inner 
world,  57. 

East  and  west  as  permanent  sugges- 
tion, 138. 

Eastern  reliefs,  351. 
Education  by  deception,  132. 


INDEX 


423 


Elaboration,  as  school  exercise,  276  ; 
pictorial,  277 ;  two  forms  of,  285- 
286;  by  catalogue,  287;  under 
limitations,  295. 

Eliciting,  153. 

Eliot,  George,  398. 

firnile,  257. 

Emotional  background,  the,  92. 

Ending,  184  ff. ;  as  termination, 
184. 

Enumeration,  289-291. 

Estimate  of  cubic  content,  377-378. 

Ethics,  268. 

Euclid,  333,  390. 

Euler's  Theorem,  33,  154. 

Exaggerations  necessary,  407. 

Example  and  precept,  268. 

Examples,  too  attractive,  398 ;  stere- 
otyped, 393. 

Exceptions,  222-223. 

Excluded  middle,  40,  86. 

Explanation,  5,  7,  8, 76 ;  subordinate, 
203. 

E '  xpositandum,  11,  161. 

Exposition,  by  pupil  and  by  teacher, 
4;  data  of,  5;  bipolar,  9;  essen- 
tially constructive,  60,  61,  63; 
destructive  stage  of,  62;  unit  of, 
64;  relativity  of,  160;  starting- 
point  of,  168;  possibility  of  too 
good,  210-211;  distinguished  from 
illustration,  18,  257;  to  class  as 
opposed  to  individuals,  225. 

Expound,  meaning  of,  2. 

Fable,  need  for  details  in,  270 ;  truth 
in,  271. 

Fact  and  faculty,  63,  162,  419. 

Facts,  explanation  and  interpreta- 
tion of,  5-6;  organised,  161;  of 
co-ordinate  rank,  201. 

Faculties,  44  ff. 

Fairytales,  272. 

Fait  accompli,  342. 

Fatigue  diagram,  384. 

Faust,  257. 

Field  of  consciousness,  67,  68 ;  84. 

Finger-post  criticism,  25,  26. 

Fixed  backgrounds,  100. 

Fluid  minds,  101. 

Focal  ideas,  67,  129. 

Foreign  suggestion,  129. 

Formal    Steps,    145    ff.;     errors    in 


application  of,    152;     in  notes  of 

lessons,  154. 
Frankland,   Dr.    Edward,    170  note, 

331, 332. 
French,  order  of  adjectives  in,  190; 

auxiliary  verbs,  393. 
Frith,  W.  P.,  347. 
Froehener,  M.,  218. 
Fuller,  Thomas,  22,  23. 
Fusion,  73,  74,  234. 

Galton,  Francis,  279. 
Gaping  Point,  163  ff.,  277. 
Garnett,  Dr.  William,  120  note. 
Geikie,  Sir  Archibald,  188. 
Generalisation,    36,    155,    199,    262, 

354;    step,  148-149. 
Geography,    183;     commercial,    182; 

text-book,  318. 
Geometry,  the  new,  184 ;  descriptive, 

333. 
German,  vocabulary,  28 ;  possessives, 

193;  rule  as  to  gender,  225. 
Globes,  the,  327. 
Glyptic  formulae,  331-332. 
Grammar,  teaching  of,  188. 
Granger,  Rev.  James,  396. 
Grangerising,  396. 
Greek  education,  211. 
Growing  Point,  162. 
Guy  Fawkes,  338. 
Guyau,  J.  M.,  127. 

Hamilton,  Anthony,  180. 

Hamilton,  Clayton,  203. 

Hamilton,  Sir  William,  40,  70. 

Hardewittes,  101. 

Harris,  Dr.  W.  T.,  142  note. 

Hartmann,  Dr.  Berthold,  98  note. 

Hay,  Ian,  222. 

Hayricks,  painted,  337. 

Hayward,  Dr.  F.  H.,  318. 

Helvetius,  406. 

Herbart,  145,  146,  147. 

Herschel,  Sir  John,  329, 330, 331,  408. 

Heuristic  method,  32,  172,  173. 

Hill,  Burton,  397. 

History,  183;  under  different  pow- 
ers, 160;  text-book  in,  293,  294; 
pictures  in  teaching  of,  338; 
"true"  pictures  in,  339. 

Hobbes,  275 ;  credit  system,  276. 

Hodgson,  Shadworth  H.,  116. 


424 


INDEX 


Hofmann,  331. 

Homer,  251,  288. 

Homonyms,  123. 

Howatt,  Rev.  J.  R.,  289. 

Hugo,  Victor,  293. 

Hume,  48. 

Huxley,    Professor   T.    H.,    48,    77 

notes. 
Hypostasis,  44,  45,  46. 

Iconographs,  139-140. 

Ideas,  40;  distinguished  from  facul- 
ties, 45;  as  material  of  thought, 
46;  as  forces,  46-47;  interaction 
of,  47;  focal  and  marginal,  67; 
realisation  of,  72,  275;  complica- 
tion and  fusion  of,  73;  as  perma- 
nent potentialities,  84 ;  in  subcon- 
scious state,  87-89 ;  complexes  of, 
98;  organisation  of,  99;  breaking 
up  of  complexes  of,  169-170;  re- 
call of,  104;  ready-made  com- 
plexes of,  99;  mediate  and  im- 
mediate recall  of,  119;  conditions 
of  recall  of,  122;  development  in 
consciousness,  283. 

Idee  fixe,  99,  100. 

Identity,  principle  of,  39;  sense  of, 
69. 

Illustrandum,  19,  28,  30,  31,  232,  235, 
241,  312,  320,  321,  327;  cognate 
with  illustration,  413;  mastery 
over,  415. 

Illustrate,  meaning  of,  18, 19. 

Illustration,  distinguished  from  ex- 
position, 18,  257;  in  a  circle,  27; 
as  a  sedative,  22;  anticipatory, 
31,  32;  twofold  classification  of, 
229;  verbal  and  material,  317; 
teacher's  use  of  the  incidental  of, 
207;  classification  of,  319;  hand- 
to-mouth  method  of,  392;  over-, 
395 ;  misplaced  pictorial,  41 1 ; 
pupils  dependent  on,  414;  dia- 
grams of,  367,  387. 

Illustrations,  interstitial,  23;  di- 
dactic use  of,  242;  misleading, 
.242;  stock  of,  393;  carried  over 
bodily,  408;  prepared  and  extem- 
pore, 419-420. 

Illustrative  enumeration,  290-291. 

Imagery,  visual,  385. 

Images,  55 ;  generalised,  56. 


Immediate  recall,  119. 

Impressionability,  threshold  of,  300; 
zone  of,  303. 

Impressionists,  336. 

Incidence  of  external  influence  in 
suggestion,  129. 

Incidental  references,  205,  207. 

Induction,  32,  33. 

Inductive  methods  of  teaching,  156, 
157. 

Inference   point,  161,  162,  277. 

Information,  153,  292,  319. 

Inhibition,  71. 

Instruction,  153. 

Inter-aims,  173. 

Intercourse,  51. 

Interest,  rhythm  of,  186;  in  relation 
to  recapitulation,  226-227;  de- 
railing of,  400;  killing  of,  404,  407. 

Interstitial,  vision,  13;  illustrations, 
23. 

Introductions,  179. 

Isocrates,  244. 

Ivanhoe,  339,  344  note. 

Jacotot,  2,  3 ;  Jacototian,  379. 
James,    Professor   William,    15,    68, 

103,  232,  233. 

Janet,  Professor  Pierre,  127. 
Joe  Millers,  religious,  273. 
Johnson,  Dr.,  132,  407. 
Johnston,  F.  W.,  22  note. 

Keatinge,  M.  W.,  129,  132. 

Key,  31  note. 

Knowledge,  reproduction  of,  50 ;  not 

yet  due,  153,  394. 
Knox,  John,  49. 

La  Fontaine,  257,  262,  263,  270. 

Lamb,  Charles,  237-238. 

Landois,  77  note. 

Language,  teacher's  use  of,  387. 

Latin,  genders,  27-28;  oratio  obli- 
qua  in,  31 ;  order  of  teaching,  61 ; 
negatives,  133,  414;  method  of 
teaching,  157;  from  abstract  to 
concrete  in,  200;  grammars  and 
exceptions,  223;  Latin  Compara- 
tive, 229;  cum  with  subjunctive, 
392;  examples  in  grammar,  398. 

Law  stage,  55. 

Laws  of  Th  mght,  40,  75. 


INDEX 


425 


Lawson,  William,  310. 
Lectures,  lantern,  23,  26. 
Lecturing,  12. 
Lesson-lengths,  173. 
Leutz,  Ferdinand,  174  note. 
Liebig,  Baron,  20. 
Listening,  analysis  of,  12  ff. 
Liverpool,  Lord,  269  note. 
Locke,  John,  41  note,  85. 
Lodge,  Sir  Oliver,  207. 
Logic,  86,  269. 
Logical  presentation,  187  ff. 
Lucas,  E.  V.,  14,  note. 

Macaulay,  Lord,  284. 

Macdougall,  W.,  10  note,  126,  127, 
388. 

Macdowall,  K.  A.,  218. 

Macleod,  Norman  Islay,  269. 

Macturk,  John,  363. 

Magna  Charta,  201. 

Marshall,  Professor,  385. 

"Match  drawing,"  382. 

Material,  319. 

Materialism,  88. 

Mathematics,  9,  61,  183. 

Mauclair,  Camille,  337. 

Maxwell,  J.  Clerk,  368. 

Mediate  recall,  119. 

Meiklejohn,  Professor,  412. 

Meno,  368  note,  416. 

Mental  activity,  116,  131. 

Mental  content,  38,  41,  42,  61,  138, 
156;  analysis  of,  167;  overlap  of, 
168;  organisation  of,  192;  com- 
mon segment  of,  225,  277;  limits 
of  organisation  of,  163,  411. 

Mental  focus,  158;  sliding  scale  of, 
160. 

Mental  harmony,  law  of,  75. 

Mental  imagery,  280-281. 

Mental  parallax,  113. 

Mental  pictures,  108,  111,  277;  ex- 
ternal standard  of,  112. 

Metaphor,  130;  as  analogy,  231; 
conditions  of,  illustrative  use  of, 
232;  dangers  of,  234;  relation  to 
illustrandum,  235  ff. ;  cumulative 
effect  of,  238 ;  one-sided,  240. 

Method,  deductive  and  inductive, 
156-157;  Socratic,  80  ff.,  96,  172, 
174-175;  heuristico  32,  172,  173; 
dangers  of  study  of,  i!6  ff. 


Metric  system,  211. 

Metrical  diagrams,  367. 

Mill,  J.  S.,  19,  200. 

Million,  meaning  of,  298. 

Milton,  240,  403,  405. 

Minds,  kinds  of,  in  respect  of  back- 
grounds, 98;  rigid,  98;  fluid,  101 ; 
plastic,  103;  the  associative,  102. 

Minimum  suggestible,  141. 

Mistake- traps,  221. 

Mitchell,  Professor  W.,  131. 

Mitchill  and  Carpenter,  4  note,  306. 

Model,  the,  317;  relation  to  real 
object,  319;  as  type,  323;  three 
dimensions  of,  324,  326,  330;  un- 
reality of,  325;  relation  to  senti- 
ments, 325;  contrast  with  dia- 
gram, 328 ;  made  by  pupils,  334. 

Monet,  Claude,  336. 

Moral,  place  of  the,  267 ;  child's  view 
of  the,  270. 

Mot  propre,  189. 

Multiplication  through  addition,  29. 

Murray,  Dr.  J.  A.  H.,  249. 

Myers,  Dr.  C.  S.,  349. 

Narrative,  203. 

Nathan  the  prophet,  214,  215. 

Nebuchadnezzar's  furnace,  300. 

Newton,  Dr.  Richard,  254,  256. 

Niagara,  301,  304,  311. 

Nicholson,  Professor  H.  A.,  59. 

Non-contradiction,  law  of,  40. 

Norris,  Frank,  339. 

North,  Lord,  135. 

North  Carolina,  area  of,  359. 

Novelist's     anticipatory     references, 

205. 
Nunn,  Dr.  T.  Percy,  206, 219, 334, 335. 

Object  lessons,  64. 

Objective  standard  in  illustration, 
344. 

Objects,  317. 

Observation  frequency  polygons,  384. 

Ohm,  120. 

Onions,  Oliver,  136. 

Order,  of  substantive  and  objective, 
190-191;  of  figure  and  illustra- 
tion, 241. 

Order  of  presentation,  determined  by 
beginning,  195;  by  practical  con- 
siderations, 208. 


426 


INDEX 


Originality  in  lectures,  14. 
Ornithorhynchus,  59-60. 
Orrery,  328. 

Orthographic  story,  180. 
Osier,  Dr.  W.,  239,  240. 

Paradise  Lost,  405  note. 

Paragraph,  the  first,  178;  illustrative 
of  bad  order,  205. 

Parallelism  between  physical  and 
mental,  89. 

Passive  poets,  341. 

Paterculus,  242,  244. 

Paulhan,  Fr.,  70,  71,  117. 

Pearson,  Professor  Karl,  384. 

Percentages  and  suggestion,  137. 

Perspective,  8,  345,  350. 

Petit,  M.  Edouard,  349. 

Pictorial,  the,  306,  355;  diagram, 
complication  of,  356-357. 

Picture,  limits  imposed  by,  340 ;  two 
conditions  of  use  of,  as  historical 
illustration,  339;  as  illustrating 
poetry,  341;  infidelity  of  illus- 
trative, 341  ff. ;  in  text-books, 
347;  distinguished  from  diagram, 
348;  informative  aspect  of,  349- 
350;  in  advertisement,  350;  clas- 
sification of,  in  order  of  abstract- 
ness,  352;  place  of,  in  teaching, 
355. 

Pictures,  mental,  277-280. 

Plastic  mind,  103. 

Plato,  250,  251,  253,  254,  416. 

Poe,  Edgar  Allan,  130,  241  note. 

Point  of  view,  1,  113. 

Polyolbion,  405  note. 

Portraits,  337. 

Preaching,  11. 

Preferred,  apperception  mass  (or 
background),  120,  123,  125;  sense, 
the,  108-109;  ideas,  68. 

Premature  conception,  214,  242. 

Preparation  Step,  147,  167. 

Presentation,  145;  order  of,  146; 
falsity  and  incompleteness  of,  219; 
logical,  187  ff.,  199;  preliminary 
conditions  of,  195;  bad  order  of, 
205. 

Presentative  activity,  66-67,  74,  120. 

Presented  content,  65,  93. 

Primary  colours,  169;  psychological, 
170. 


Primer  on  Teaching,  387. 
Problems,  182,  217. 
Prompting,  135. 
Pseudo-auto-suggestion,  129. 
"Psychic  fringes,"  284. 
Psychology,  86,  268;  of  listening,  12. 
Pupil,  as  technical  term,  11. 
Purpose  unit,  173. 

Qualitative  and  quantitative  reason- 
ing, 385. 
Quotation  marks,  394. 

Ramsay,  Sir  W.,  318. 

Raven,  Rev.  J.  H.,  31. 

Reading,  14. 

Realising,  ideas,  72,  275;  figures, 
291 ;  sizes  and  numbers,  297. 

Reality  in  models,  325. 

Recall,  104;  conditions  of,  122; 
mediate  and  immediate,  1 19. 

Reconstruction,  214. 

Redintegration,  134. 

"References  forward,"  207. 

Relative  sizes  of  countries  and  conti- 
nents, 359-304. 

Relativity,  in  exposition,  160;  in 
manipulating  vast  numbers,  309— 
311. 

Rennet,  Dr.  David,  213. 

Republic,  the,  250. 

Rhythm,  of  attention,  157;  in  teach- 
ing, 179;  of  interest,  186:  of  ab- 
stract and  concrete,  199. 

Richter,  Jean  Paul,  235  note;  268 
note. 

Richter,  Karl,  173  note. 

Rickerton  Medal,  176. 

Riddle,  240. 

Right  and  left,  confusion  of,  114. 

Rigid  minds,  98. 

Romanes,  G.  J.,  349. 

Rothschild,  Nathan,  267,  269,  270 
note. 

Rousseau,  257  ff.,  326. 

Rule,  and  exception,  222  ff. ;  and 
example,  228. 

"Rules,"  222,  282. 

Ruskin,  8,  298. 

Saving  pupils  trouble,  210. 
Scansion,  216. 
Science  teaching,  217. 


INDEX 


427 


Scott,  Sir  W.,  237,  339,  350. 

Self-activity,  130. 

Self-referent  tendency,  265. 

Sentences,  loose  and  periodic,  248. 

Shadows,  colour  of,  246. 

Shakespeare,  15,  25,  78. 

Shelley,  15. 

Sidis,  Dr.,  132. 

Silhouettes,  Chinese,  140. 

Silvestre,  M.  J.  B.,  139. 

"Simple"  and  "easy  to  understand," 

198. 

Simplon  Tunnel,  182. 
Sirius,  309. 

Socrates,  80,  250-251,  416. 
Soft  pedagogy,  212. 
Spencer,  Herbert,  76,  169,  189-190, 

196, 197,  198,  205,  214,  246,  279. 
Sprachgefiihl,  44. 

Standard,  area,  315,  360;   for  differ- 
ent powers,  160;  map  of  West  of 

Old  World,  380. 

Starting-point  of  exposition,  167. 
Static   view   of    concept   and    inner 

world,  57. 

Stephens,  Winifred,  294. 
Stevenson,  R.  L.,  271. 
Stirling,  Hutchison,  277,  278,  280. 
Story,  three  uses  of,  251;    the    in- 
vented, 271 ;  sources  of,  273. 
Stout,  Professor  G.  F.,  42,  116,  128, 

284. 
Straight  lines  in  diagram,  353,  371, 

378. 
Stun,   Threshold  of,   301,   302,   303, 

304,  306,  307,  313,  412;   raising  of, 

305. 
Style,   test  of,    7;    underlying,     16; 

philosophy  of,  189;    allusive,  403, 

405. 
Subconscious,     the,     85;      physical 

correlate  of,  87-88. 
Subjunctive,  222,  392. 
Substantive,  elements  of  thought,  43, 

73,  125;  meaning,  123. 
Sufficient  reason,  law  of,  40. 
Suggestion,  external,   122;    Wundt's 

and    Thomas's    definitions,     128; 

Baldwin's  and  Janet's  definitions, 

127;     auto-,    128;     foreign,    129; 

pseudo-auto-,  129;  unilateral,  133; 

relation     to     apperception,      134; 

permanent,  135,  159,  371 ;    moral 


justification  of,   143;    as  an  end, 
143—144 ;   most  obvious  kind,  350. 

Superlative  references,  404. 

Superstition,  one  function  of,  75. 

Synthetic  step,  147. 

System,  stage  of,  55;  step,  147,  149. 

Tactiles,  109. 

Teaching,  six  principles  of,  196-197; 

criticism  of  six  principles  of,  197 

ff. ;   by  text-books,  318;   deductive 

and    inductive  methods  of,    156- 

157;  to  class,  226. 
"Telling,"  153. 
Temptation,  144,  256-257. 
Tennyson,  235,  288,  402-403. 
Theory  and  practice,  419. 
Therefore,  use  of,  165-166. 
"Thing  stage,"  44,  55. 
Thing-in-itself,  53. 
Thinking,  atomistic,  15 ;  small  change 

type  of,  277;  pictorial,  278-279. 
Thomas,  Professor  P.  E.,  127. 
"Thorough,"  159. 
Thought,  laws  of,  39,  75;    swiftness 

of,  281. 
Threshold,  85 ;  of  Consciousness,  86  ; 

of  Impressionability,  300-303;    of 

Stun,  301-307,  412. 
Time-unit,  174. 
Transitive,  elements  of  thoughts,  43 ; 

meaning,  125. 
Trapp,  E.  Ch.,  171. 
Turbid  media,  91. 
Type,  the,  as  illustration,  247. 

Unconscious  humour,  411. 

Unit,   time    and    purpose,   174;    size 

of,  204;   general  treatment  of,  204; 

highest  available,   315;   standard, 

315-316,  360. 

United  States,  area  of,  364. 
Units,  66. 
Unstable  backgrounds,  102. 

Vacuum,  the,  in  exposition,  216  ff . 

Velasquez,  337. 

Veronese,  339. 

Virgil,  105. 

Vision,  interstitial,  13;  field  of,  14. 

Visuals,  108. 

Vorstellung,  278,  283. 


428 


INDEX 


Wallas,  Graham,  384-385. 

Walpole,  Horace.  284. 

Ward,  Dr.  James,  386. 

Weariness  from  over-correlation,  27, 

400. 

Webster,  dictionary,  17,  249. 
Wells,  H.  G.,  301,  304. 
Whately,  130  note. 
Whitman,  Walt,  287, 288, 346. 
Whittier,  171. 
Wight,  Isle  of,  314. 
Wilmann,  Otto,  196. 
Witmer,  Lightner,  171,  359. 


Witt,  Robert  Clermont,  348. 
Wolf,  Lucien,  270. 
Wordsworth,  99,  271. 
Worlds,  inner  and  outer,  51  ff. 
Wright,  Professor  Mark,  12. 
Wundt,  128,  129. 

Zidangabe,  171  ff.,  175,  184,  268. 
Ziller,   Tusikon,    171,   174    note,   197 

note. 

Zone  of  impressionability,  303. 
Zivischenziele,  173,  176,  185. 


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